They did, in summer 2007. They priced it for a dollar less than Netflix. They stuck with it almost 6 years, ending it when they left the retail business (except for the one franchise store remaining in Bend, Oregon).
I think Blockbuster was an anti-brand at that point because of choices they made to navigate having national brick and mortar shops, making an unknown startup more trust worthy.
I'd used them begrudgingly in places that had no independent shops and the various inventory they didn't have were usually rumored to be that their management was christian conservatives, though I think it was more that they avoided a few arbitrary hotspots of potential conservative boycotts that would hurt them in other regions.
I remember that when a friend suggested them, I was quite pleased to be paying $1 more not to help them.
https://www.reuters.com/article/industry-blockbuster-dc/bloc...