Was literally looking over that part in FMC last night and it did strike me as a bit odd, my immediate thought was to things like the parrying dagger. A weightier thing like a polearm wouldn't be able to parry a dagger too well when in close combat unless imagining the pole part being used to absorb the cut from the dagger. I guess on the opposite end, though, I find it hard to imagine daggers doing too well against a polearm. Once they get far enough apart the techniques are drastically different.
I see what might have happened, given the wording in Chainmail, but it does seem like the faster (lower classed) weapons get a chance to parry, originally, as you said. The problem here is, it seems odd that weapons with a higher class, with their pretty much sole advantage of attacking first in the initial engagement, seem to lose that advantage with this subsystem, given the language about "first blows" seeming to mean the first strike of the engagement. I feel like it makes sense if in close combat already, where both opponents could already reach each other, but the initial chance to hit should go to the character with more reach, I think. It does seem like it makes an exception for pikes, spears, and lances (but not polearms apparently): if there's a charge, then those weapons get priority in the first round, but I feel like I'd want to expand on this.
Combine this system with the generally rougher time lighter class weapons get versus most defensive types, though, maybe it evens out?
I'm glad you brought this up.