Teams don't keep track of it, but we do. This site is functionally a part of Sports Info Solutions, which tracks any information like that that we can think of to track, and then sells the information to the teams. So.. .yes, we know.
Your point is a good one, and this is a significant analytical quandary, how to handle this. To start with, first basemen are often sluggers because one CAN play first base even if you can't run and can't throw, so players who can't run and can't throw often wind up at first base. Because that is true, the offensive numbers of first basemen are always high. Analytical logic, related to the defensive spectrum, assumes or sometimes assumes that if the offensive contribution at a position is high, the defensive contribution at the position is low, and this is SOMETIMES very true; that is, there are many first basemen who make a very limited defensive contribution.
Nonetheless, it IS true, I think, that the defensive delta at the position is enormous. (We have been witnessing this day to day on the Red Sox, where Dalbec has been in a season-long slump, so Franchy Cordero has been playing half the time at first base. They're trying to get Cordero to achieve the potential he has been wasting for five years, and making actually pretty good progress on that, but anyway, Dalbec once he gets a little experience will be Don Mattingly at first base, and Cordero is just God Awaful there, so all kinds of costly crap happens to the Red Sox when Cordero is at first base, and you always gnash your teeth and wish Dalbec would start hitting.)
Anyway, it could be an overstatement that first base is defensively more important than, let us say, shortstop or third base; it could be an overstatement, and I think that it is. But it is true that the defensive contribution of the first baseman is historically undervalued in analytic systems, and also true (b) that this is very hard to avoid, and (c) that the real defensive value of a first baseman is hard to measure.
In Win Shares, I gave some credit defensively to the first basemen if the number of errors by shortstops and third basemen on the team was low. But this honestly is as much desperation as anything; since the defensive values of first basemen are so hard to measure, I'll try anything to fill in the gap.
The Pete Palmer system for rating defensive first baseman is just horrible, horrible, horrible, just absolutely and completely dysfunctional. It relies heavily on ASSISTS by first basemen; since putouts by first basemen are 90%+ secondary plays initiated by someone else, Pete switched to assists. But assists by first basemen are discretionary, since there are about 100 plays per season on which a first baseman can choose either to touch the base himself or to flip to the pitcher, thus getting an assist. So there is basically no correlation at all between first base assists and first base defensive contribution.