Which option is better depends on what games you want to play and your local network.
I think it's a fine idea, but as others have stated it depends on your network. If you have a PC already with steam, it might be worth trying the steam link app and see how it works.
The steamdeck is going to give you more flexibility, and work around any network issues you might have. Again, depends on the games, but in general it's a great device and you can take it with you. That said, it's struggling to play some of the newest AAA games on launch, though patches do eventually seem to come to help it out.
fwiw, valve seems to believe it's got another few years in it. They've said they might do a battery/screen refresh, but the processor and such sound like they're hear for another year at a minimum.