EDIT -> @OP: Many perks have "cross-class" requirements for skills and SPECIAL stats that aren't exactly what they would seem to need. Agility governing speed and Slayer giving you a speed increase to your attacks makes perfectly fine sense to me. No doubt to make you create a more well rounded character than one focused only on a few areas.
That would be a good way to explain why this perk requires
Agility,
if this were a new perk, but it's not. Let me just say again the
Slayer perk in Fallout (and Fallout 2) was designed to require stats from a
Melee/
Unarmed (or
HtH) build. It just was. It complements those stats perfectly, so there's already a reasoning behind it. High
Agility and movement speed I guess helps with
Melee/
Unarmed, but for my play it hasn't been a noticeable increase or benefit. I mean either I'm already in melee range or I seek cover and wait for them to come to me. Why run with my minimally increased movement speed into the direction of the bullets? Also, does
Agility increase
Melee/
Unarmed attack rate on its own? That would be a benefit along with this perk, but I haven't heard that it does. In the end, you're implying that the SPECIAL and skill system is designed to pigeon-hole players into building hybrid "Jack of all trades, master of none" characters. I don't agree with this. Some people just don't want to play "well-rounded" characters.
You also said many perks are like
Slayer, and "have 'cross-class' requirements for skills and SPECIAL stats." What other perks are like this? Do you mean perks like
Chem Resistant,
Pyromaniac,
Hit the Deck that require a sort of role-playing to recognize the connections? The problem is these are not many. These are the exception. Maybe you can list more, but I really don't see "many".