I think that it is partly the ongoing nature of the task, and also what you have written about him in your posts.....
So, if you were a landscape gardener, you might get paid for sorting out his garden into something lower maintenance and tidy (so a one-off, project), and then you might agree to review it every spring and autumn. But in-between you'd expect him to mow the grass, dead-head the flowers and at least pick up any rubbish that got blown there. And... there is a limit to how fast the grass and plants grow. Ditto with his hair - he couldn't make it grow any faster, by being lazy or busy.
However you have said that he had a sink full of dishes, and a kitchen sink you had to clean before you could cook. I think that is what's worrying. You're not talking about someone who is simply too busy to iron flannelette sheets, or hoover under the sofa (many people wouldn't do that), but it sounds like he is too busy, or too disinterested, or too lazy to even take care of basic cleaning. I understand not having 3 hours to clean the whole house, but does he not even have 10 minutes to wash the dishes? Would you be going in every day to wash the dishes, or would he leave them for you all week? Does he pick up his clothes, put them away, wash and iron them? Does he get rid of rubbish, put the bins out? None of these are very exciting and maybe he would find himself too busy to do any of those too.
I know that before our cleaner comes, my dh and I have a good tidy up (it's a good discipline for us) - do you think your boyfriend would do that? We also always wash the dishes before the cleaner comes - he is not here to clean up after us in that way. However if I find some area that has got overlooked by my cleaner, then I either do it myself, or I specifically point it out to him and ask him to give it some attention. How do you think something like this would be resolved? Maybe easily, and with good grace, or it might be more tricky.
But if he doesn't clean, or garden, or update his technology or take particular care of his grooming (hair), then it sounds like he needs a full-time housekeeper, or a butler, or a concierge, or a parent.