Gamefly has historically been very slow for me. I've renewed for free and moved multiple times since I first started using them in 2011. Each time, I notice a trend of them sending my first choices out right away. After I beat the first game and send it back, though, the next game might take two weeks to get to me.
The last promo I did was in summer 2020 when they had the two games per month for a dollar. Thought I'd give them a shot and continue my subscription after the first month, so I kept the $22 per month sub. The next set of games I beat within a week, but it took two weeks for me to receive the last games. I was only able to play through two and a half games. Canceled after that.
They just seem to not have enough warehouses in the US. Or if they do, then they need to disperse inventory evenly among them. I shouldn't have been waiting for games sent via regular mail from the midwest when I live in coastal New England and there's a time factor. If UPS solves that issue considering the last presidency crippled the post office system, then maybe the change is for the better.
EDIT: As an aside, I don't see their physical media service lasting much longer. Game Pass and PS Now are essentially the same and games can be played within a few hours. There's a subscription fee, but a comparatively nonexistent wait time and no requirement to send games back lest you be charged MSRP. You want movies? Redbox has that covered, too. The only bonus to Gamefly is the ability to rent Nintendo games. And if Nintendo ever started offering current gen games as part of a digital sub, then any physical rental retailer would be in trouble.