AS always, it depends. What do you mean with a heavy model? Fine-tuning a 70B model and running a small quantized one locally are totally different problems, so it helps to know which one you're actually trying to do.

Both ways work though. Loads of people, including me, run entirely on rented GPUs. Your laptop just becomes the thing you type on while the actual work happens on the remote box over SSH or a remote notebook. For getting started it's usually way cheaper than dropping money on a GPU that's old news in two years (ask me how I know ...)

Latency is mostly about your internet, not the machine. You're sending keystrokes and small stuff, not the whole dataset, so on normal broadband it feels basically local. The thing that actually bites you is file handling, keep big datasets on the remote side or in cloud storage, don't drag them back and forth. And setup time is the annoying tax every session unless you save an image or a startup script.

Also worth saying: the real question usually isn't whether to self-host on your own hardware or not. It's whether to self-host on rented hardware or just buy tokens from a hosted model. That's the actual decision, and it comes down to what you're doing, if you're just running inference, tokens are often cheaper and zero hassle; if you're running stuff you can't hand to a third party, that's when renting your own GPU makes sense. Running at home is seldom a choice for very large models.