My employer wants us all to use laptops too. Dislike them intensely. I am able to use my desktop until they decide to take it away. No I wasn't given special broadband either, have to use my own. That said the company can provide broadband at a decent price if I want to agree to all the conditions.
I think it is getting more common. For my part because I have a desktop, after lugging the laptop in every day for a couple of weeks doing my back/shoulder in I realised I hardly used it, and it stays at home now. I can bring it in if needed.
I can see it benefits the company but I don't approve of the imposition. Bad enough if it were in place before one was employed, a right cheek to impose it afterwards. But I think you may have to live with it. The way things are gonig the boundary between personal space/time and work are getting blurred.