I had a friend who had an unhealthy obsession with the Axman. Part of this was that he thought TSM (which he custom installed on his campaign mech) actually tripled damage, rather than doubling it, but even so its not a great mech, and I had to beat the pants off him a fair few times to convince him that a slow short ranged mech wasn't the best idea.
I'm not a huge hatchet fan at the best of times, but the Axman just makes too many mistakes. I get the coverage angle, but given a choice between the lasers and the hatchet, I'd chose the lasers nearly every time unless my heat was way in the red. If they'd wanted to pair the hatchet with LRMs, maybe I'd get that since the odds of wanting to use both would be a lot more ridiculous, but the MLs would have been a third of the mech's close in punch if they could be used in conjunction with the hatchet.
As for everything else, the LRM/AC20 switch is six of one, half a dozen of another. It moves the mech from one role it does only semi well into another it does only semi well. As a bodyguard, the hatchet is still the wrong choice, since most mechs that can slip past/through/around your lines to get to your missile mechs will be fast, and the Axman can't easily run down fast mech to employ its hatchet. The LPL is the right choice for that, for the same reason, so the mech is still usable in the bodyguard/support role, but not through any benefit of its signature weapon.
I do think that, as was pointed out, the hatchet is most useful against people who have too much respect for it. It has a nasty reputation in some circles, and if you can intimidate someone with a weapon that thanks to your ML placement you'll never use anyway, so much the better. But still better to just chose a mech that sinks that dead weight into armor or an SFE or more guns.