Guess we have different playstyles. I can't even imagine having an idle diplomat. There are always relations to be improved, claims to fabricate, the next vassal to target... Those slots are absolutely precious to me, and the diplomats only slightly less so. I suppose if you always play a nation like Portugal and ignore Europe completely, you might have less of a need for them, but I'm not sure a United Scandinavia has diplomats and relations slots to tie up for decades (I rarely do no matter who I'm playing).
As for the argument to conquer, rather than vassalize. I remind you that I prefer vassalization, too, I simply can see situations where conquest/coring would work as well or better. You're repeating admin point saving that are inflated (go check), especially if one is just targeting the gold provinces. New world provinces are cheap to core, if you're doing it right. Yes, you'd still be talking about close to 500 admin points, but only if you're talking about all of Central America. But admin points aren't the primary driver for me, when I vassalize. Time is. If I'm in a position to core the gold provinces using admin points, and that would be quicker, I would certainly do that. Admin points are also just not as precious to me as they appear to be to you. I find diplomatic points are usually my bottleneck, but maybe it's a function of which ideas we prefer or other elements of our play style.
Yeah, after playing a pure colonization game a few times, it gets a little old. I don't do it exclusively anymore, either, I tend to do it in conjunction with my European ambitions.