If he just wanted to ensure EVERYONE thought him dead he probably would have offed Cadsuane when he realized he (yet again) completely failed to fool her even for an instant. His PoV shows he knows his Warder Sedai are quite aware of his little Face Off maneuver. Speculating on whether any or all will trail after him and (yet again) considering the morality of continuing a relationship with more than one of them demonstrates he is not just abandoning them. Regarding Elayne specifically, you pretty much stated why it is unthinkable he meant to abandon their kids before they were even born (because "deadbeat dad" makes the most sympathetic Christ figure, right? ) Likewise, all the grief/relief of his separation and reunion with Tam makes it unlikely he would simply let his father believe him dead either.

I think the whole thing was meant to be a temporary arrangement, possibly combined with a solitary and long overdue vacation. His three lovers provoked universal surprise and some disgust with their nonchalant reaction to his death (which was kind of stupid if they want to convince peoples his death was genuine.) Multiply that by Tam, Mat, Perrin, Moiraine, Thom, Loial and all the rest of his close friends/family and he would be Randland version of Elvis. Moiraine, Thom, Tam and Elayne could fake it convincingly, and maybe Mat, too, by this point, but... Min? Nynaeve? They suffer the weakness common to painfully honest blunt people: They literally cannot dissemble to save their lives.

There is a reason the women who Bonded him immediately start plotting how to convince everyone he is really dead. An anonymous stranger having private chats with each member of his inner circle in the first days following his death could not help drawing suspicion. That would be bad enough by itself, but there is the added risk that any surviving but undetected Darkfriends/Dreadlords/Forsaken like Moghy might recognize Moridins face. That is a potential problem whatever he does and wherever he does it, but the closer he is to the various centers of power the more likely he is to encounter a Shadow mole high ranking enough to have met Moridin on multiple occasions. For that matter, it is not even certain he knows Graendal and Lanfear are dead—but he DOES know any surviving Forsaken are likely to seek vengeance against him, and seek him at the rarefied levels of power to which the Dragon Reborn and his consorts are accustomed.

On that note, there is no reason to think he means to abandon Elayne or Min forever (and his final speculations about them suggest just the opposite,) but every reason he would not want to immediately jump into the center of Andoran and/or Seanchan court life. Many people already openly discuss their apparent apathy toward his death before his body is even burned; it would be deeply suspicious if either took up with a new paramour the next day, and the eyes of ever Andoran and Seanchan noble will be on them for the rest of their lives (unless, of course, they fake their own deaths, too.) In the specific case of Tuon, integrating Rand as her Doomseers husband without her summarily executing all involved to save face would be a delicate and extended process.

My personal view is that Rand intends MOST of the world to believe him dead, but is only leaving his inner circle out in the cold long enough for a solitary stress free sabbatical. I would not be surprised if his harem ends up letting Tam, Nynaeve and the other ta'veren in on the secret pretty soon, but they probably want to give him time to exit stage left lest anyone is tempted to follow.

Anyway, Egwene is dead, so why are you complaining?