Different pitchers allow different HR/FB, this stat shouldn't just be neutralised.
Most pitchers allow league average over multiple seasons though. Pitchers have some control over HR/FB, LOB% and BABIP but obviously ERA is a terrible stat because all of these things vary a lot season to season. FIP corrects for 2 and ignores the 3rd which is just as terrible. HR/FB most certainly should be neutralized just as much as LOB% or BABIP though, it is no different than those. It would be better if they were regressed towards the pitchers career numbers but we don't have anything that sophisticated to use.
I generally look at the yearly xFIP trend. If a players xFIP is improving each year than he is improving even if his ERA says he isn't. If his xFIP is going the wrong way then I will avoid him. To me FIP is mostly useless, a stat that corrects for 2 things but not the 3rd is just not going to be useful to me, it is picking out the pitchers that got lucky with HR/FB and telling you to avoid the ones that had bad luck with it. tRA is too busy deciding how good a pitcher's results were for a year and not trying to isolate out the variance.