Hello, thank you for the question.
You are correct, the work of other websites done for commercial purposes is almost certainly under copyright.
If you can get their permission to use images of their work, then go ahead and use it.
But it's not "fair use" to use the copyrighted work of others to advertise your own commercial enterprise, especially when that enterprise is to very possibly compete with the copyright holders.
It's very possible that the site owners hold the copyright, that it was transferred from the designers to their employer or contractor. But even then, if the owner stands nothing to gain then why would they agree?
Why not do some free designs for a charity? You'd get your name out and have your own legitimate work to put into a portfolio.
Anyway, you could do as you have suggested but you're leaving yourself wide open for a lawsuit.
Anything else to discuss? If not, may I have a positive service rating please?