The problem you have is that you're talking about professional teams, the best of the best, where each player is among the 32 or so best at their position (for positions with one player, anyway) in the world. The level of ability at their very precise skill is extremely high - and because of the amount of work needed, everything else is, for the most part, left aside.
College is entirely different - most college teams have a field goal kicker, but most of them are not nearly on the same level as a pro; not only are there only 32 professional kickers (give or take), of which maybe 25 are year-to-year-consistent, but field goal kicker is one of the most long lived players in the NFL - they can kick into their 40s, a career of nearly 20 years, if they're good! So maybe two kickers a year, at most, come out of college. Everyone else in the college ranks is not good enough - and for most college teams it's a huge difference. Few have a kicker who is reliable even from 35 yards. See this article which shows "power 5" (the very top schools) kickers are only 71% from 35-39 yards, for example, and would make only 83% of extra points (30-34 yards) in the NFL. Not horrible, but again these are people practicing kicks, and they're the top of that group - and they're only taking kicks their coaches think they can make, so the teams that have worse kickers don't try them from that distance as often.
It's not that different from pitchers and batting in the MLB. Sure, a few pitchers have some skill at hitting - Otani, for example - but, for the most part, pitchers are terrible hitters. That's because the skill is so different that what makes them, physically, incredible pitchers doesn't really correspond to making them good hitters, even if they practiced a lot - which they don't, because that would take away time from pitching practice. It's so incredibly rare to find someone who has both kinds of physical gifts, winning the lottery twice, basically.
The same goes for punters and kickers - while there are some corresponding elements, kicking field goals is really hard. Even the best kickers have bad days! It takes an incredible amount of practice to be able to hit a 35 yard field goal - it's not just leg, it's having a super consistent action and a huge amount of built-up muscle memory. Leg helps, of course, but it's not nearly the same as a punter - who needs some accuracy also, of course, but a very different kind of muscle memory goes into punts.
So, why don't they have a punter who can also kick field goals at a professional level? Because those people don't exist, and it's not worth it to find those people who are slightly worse punters and somewhat capable field goal kickers - as they wouldn't have a job more than once every few seasons.
And one other thing to address - "they are 18/20 of the top scoring players" - that's pretty meaningless in the NFL. No quarterbacks are on that list, but that's because they don't get credit for "scoring" points for their touchdown passes, or their handoffs, or whatnot - only if they actually score. It's like saying 1B gets the most putouts, by far, in baseball... it's true, but it's nearly irrelevant; they're doing a small amount of work, while the 2b/ss/3b is doing the majority of the (difficult) work. I'd still rather have a good fielding 1b for sure, but it's not really accurate to describe them as the most important fielder!
Kickers score the most because there is only one of them, while there are multiple of every other position that actually scores. Many of those points are extra points, which can be totally disregarded - the average team would, actually, be better off going for two anyway! So you do miss some field goals, but even then many of those aren't really adding much in the way of marginal points; some in fact are kicked when the expected points from that down and distance are more than three! Teams can, and do, win without a kicker that can kick at all, and while it's better to have a good kicker of course, it's by no means the end of the world if your kicker gets hurt in-game.
