I never knew there was any other way to settle draws in single knockout matches. The World Cup does the same as UEFA competitions. I guess the question thus boils down to why Copa America does it differently.

I Googled, and NYT has this to say on the matter (regarding no extra time, straight to penalties):

"This has long been the format with the final also using the same rules between 1995 and 2004. The only tournament where extra-time was used for each knockout round was 2011 before returned to previous rules at the next edition in 2015."

As for the rationale behind it, I guess TV scheduling is easier if each game is just 90 min + possibly penalties rather than an extra 30 mins as well. Having extra times is also quite tough on the players, especially if it happens more than once to a team.