And in time other Houses will increase their power with the spoils, and gain Great Houses status eventually, and replace the others. We were told it's always been the way things have been in Andor, Houses rise and fall and fluctuate in power through the centuries.

There's no fixed limit to the number of Great Houses (it's just a matter of how many smaller Houses recognize a House as such - Elayne punished rebellion and attack on the capital by stripping two Houses of their lands, but it's what comes next, the lower Houses aligned with them scattering to support another House that will be their real demise), and Elayne didn't strip of their lands nearly enough Houses to make a big difference in the balance of power, all the more since the most powerful Houses of all accepted Elayne as Queen and sworn fealty to her as sovereign, but aren't exactly her lapdogs.

Elayne has not "granted herself the right". It's what always happens when the succession turn to war between the Houses. She did nothing the law of Andor didn't grant the Queen of Andor. She rather did what was expected of the sovereign. Some close to her think she's been too lenient for Andor's own good, especially with those that were not at the gate that morning because they had betrayed their allies and stood aside to see who would win.

Elayne was the next Queen of Andor by Andoran Law, there shouldn't have been a Succession in the first place, the support of ten great Houses merely a formality, unless ten Houses decided for a change of rule and named a new heir (which no ten Houses have done). Dyelin as Regent even had those who rose against Elayne's legal right imprisonned in Aringil. The Houses that opposed her went knowingly and openly against the succession law by taking arms against the rightful heir. They knew the only way they could get away with it was if they or their allies won and the new Queen they put on the throne "overlooked" what they had done. They knew from the start the very fate of their Houses was at risk if they failed and Elayne or some of the others (like Dyelin, like Pelivar's group) won without dirtying their hands, just like Elayne herself knew that not only the throne but the future of her House hung in the balance.

Elayne didn't have much of a choice anyway, not bringing down these Houses would have undermined Andor's stability. A Queen can't easily pardon rebellion, especially among the powerful, without justifying it. The Great Houses offer some check to the power of the Throne. Enough of them can remove a Queen, or refuse an heir take to the Throne, and in a way they are also the ones with the power to do something if the Queen doesn't follow the law of the Land. Andor is not an absolutist system, the Queen is bound to the law of the Land. It's not a parlementary monarchy either, most of the power resides with the Queen.

If you're talking about the "rebellion" in the Two Rivers, I wasn't aware we were supposed to take Elayne's side or to adopt her views of the situation... It's not black and white. Andor is populous and rich, but like all the other nations its population is not what it once was, and is scattered accross a much too large territory. The Throne no longer has the means to administrate the fringe regions like the Two Rivers, and only hang to Baerlon because of its strategic industry and position. They don't get the services other areas of Andor get, but they're not collected for taxes either. As sovereign, Elayne could not afford to let the Two Rivers rebel and secede, not without risking the situation become an example other regions would follow, and Andor would turn into a mosaic of de facto small kingdoms, where powerful enough nobles refuse to follow the Throne (in short, turning Andor into another Murandy). Negotiating a settlement with Perrin isn't the same as letting a rebellion (that's not even started, anyway) go unchecked. RJ gave us Elayne's motivations to react as she did, but by and large it's the situation of the Two Rivers, neglected by the Trhone, he showed in the most sympathetic (and "American" way, with their local micro-democracy and all (they "elected" Perrin as leader after all, the populace and the elected authorities in every village alike). That it did not lead to an actual secession owes much to the fact this is a story where the characters are expected to put aside, or on the backburner, even their rightful battles like this one to face the apocalypse together as a unified humanity. It was fairly obvious it wouldn't end in secession, with Perrin fighting so hard against the whole notion.

I wouldn't read monarchist sentiments on the author's part, it's pretty clear his heart was with the TR and their independant spirit (and if anything, I wouldn't read an analogy between England and America and the war of independance in there, I'm pretty sure RJ had far more in mind South Carolina and the US federal government). RJ's views on nobility and monarchies that seem to transpire from the series is that it's a huge lottery. When you have a "good" monarch (or noble), who understands why he's in that position and pays back by adhering to his duty as leader, you win and the system works, but for each Bashere, Berelain, Elayne, Dyelin you have tons of nobles who follow strictly their self-interests and refuse their duties. It's not very much a commentary on the respective values of monarchies vs. democracies, it's all far more a commentary on power and how it's exercized. RJ put a great deal of emphasis on how well educated/groomed those who have to exercize power must be. It's not really "un-American", in fact a very great deal of the values carried in WOT are very American, from RJ's near obsession with checks and balances to the way nearly all the "good" characters are expected to act as if respect for a noble/ruler is all about the position, not the person, and to interact with one another as if social classes barely existed or could easily be brushed off. Bashere welcomes a blacksmith son in law hinting that nobility is about duty and if you look hard enough you'd find a commoner put in the lead and becoming "noble" in the founding of all Houses, Galad and Gawyn fantasizes about a village girl who becomes Elayne's close friend, alonside a horse groom and an Aiel savage. Unlike Elayne and Rand, for Gawyn, marrying someone like Egwene means his line will count as commoners (She has not a drop of Ishara's blood), no longer holding any power or able to marry any noblewoman, but that issue isn't even raised in the series - even Elayne is beside herself with joy at the prospect of Gawyn and Egwene as a couple (you would rather have expected, in a real world setting, that Elayne would at least have lamented the fact she lost Gawyn for a political wedding between the future First Prince and the daughter of a House with a strong bloodline, Norwelyn for example). But for the most arrogant and unsympathetic nobles (also usually the ones who don't do their duty while enjoying way too much the benefits), "lowborn" isn't such a big stain, they mostly worry about stuff like lack of social polish, education, decorum or manners. Berelain made fun of Faile as a farmgirl, but intended to marry a blackmisth.... The social outlook in WOT is very "modern", but in the first place it's very American. If they've not precisely invented them, they're the first to have put these social values in application.

An European writer would likely have shied from this, seing it as too unrealistic in a world still totally in the grips of "old regimes" and class prejudices. RJ dealt with that in part by throwing Artur Hawkwing and his nearly modern vision of rulership into the mix.