As for minor issues, EGS does not have feature parity with Steam or GOG. They don't have user reviews, for example. This makes it a worse user experience.

More importantly, Epic has a habit of anti-competitive or anti-consumer behavior. When EGS first launched, they were keen on doing console-style timed exclusives, even for games that were already purchasable on platforms like Steam.

Lastly, Epic has a history of neglecting or shutting down games. A few of their older games were taken offline permanently when Fortnite started gaining traction. They then purchased a few studios, namely Psyonix (makers of Rocket League), Mediatonic (Fall Guys), and Harmonix (Rock Band/Guitar Hero series). These studios seem to be a shell of what they used to be. Psyonix's first major project under Epic was Rocket Racing in Fortnite, and this project seemed to be prioritized over Rocket League and even caused the removal of core features of Rocket League. Harmonix worked on Fortnite Festival, but that came at the cost of Fuser, which shut down and was delisted about a year after launch. As for Mediatonic, I don't think they worked on anything else yet, but a large portion of the studio was recently laid off. Needless to say, fans of the affected studios aren't happy with Epic as they're being treated as 2nd-class citizens compared to Fortnite players.