Opinions obviously vary. For the exact application you mention, it probably does not make that much difference (provided the boiler electronics are happy with a floating supply).
As has been alluded to, the main theoretical hazard of a floating supply arises if two Class I appliances with 'exposed conductive parts' are plugged into it. In an (incredibly unlikely) scenario, an L-'E' fault in one of them and an N-'E' fault in the other could result in full supply voltage appearing between the casings of the two appliances (hence a problem for anyone who touches both!), with any fuses, MCBs or RCDs being oblivious to the existence of any problem. One could, however, argue that one might be more likely to be hit by lightning than to encounter that pair of simultaneous faults!
FWIW, as I've said, for my standby genny (essentially like yours - primarily for boiler and CH controls etc. plus a few lights, but also a few sockets around the house - which could theoretically be used for anything), I've done (3).
Kind Regards, John