A lot if the issues currently with 2D hand drawn animation is that they are teaching it less in the US which leads to a lot of the work being out sourced.
People ask why Disney doesn’t return to 2D movies, and the simple answer is they no longer have studios or trained animators for it. Versus places like France or Japan where these types of studios are still available. Tho some anime is still out sourced to places like Korea, China, or the Philippines.
When it comes to what studios pick, I’ve hear that stop-motion is the most difficult to work with. 3D can be pricey however it can result in very detailed work. I think the reason why it is so popular with US studios is because they want their films to be a visual spectacle. There are some cheaper 3D animation software which has allowed smaller studios to pop up because all they need is a few computers.
2D puppet animation might be the cheapest and easiest to work with. That is why it is so popular with television shows and web animation.
Honestly, I think the nicest looking animation was during the 90s and early 2000s at Disney and Dreamworks. They had hand drawn animation with digital coloring and used 3D to enhance some scenes. I feel now that mix animation just looks better. Like in the Spiderverse films or tv shows using a mix of 2D puppet and hand drawn.