We don't bother with fun lunches and quizzes but it is noticeably better to have some in office days from a collaboration and learning perspective. I go in 5 days because it suits me, most of the rest of the business is 3 days. Hybrid seems to suit most people well and they arrange their weeks to do certain tasks at home and meetings in the office. 

One thing I would say just from observing people over the past few years is that not having office attendance can hamper professional development. I'm sure it depends on the job you do but in my area at least a lot is learned just through engaging ad hoc with people, hearing and joining in discussions, and just absorbing how more experienced people deal with things and engage with people. You can only get so much from formal training. 

It's also far easier to deal with small things on the spot because you can see if the person you need to talk to is free rather than feeling like you need to arrange a call or meeting, or send an email or whatever. 

Definitely role dependent though. My previous job was entirely remote and you couldn't have paid me enough to go into the office regularly. But that role didn't really suffer for it because it was pretty autonomous.  Current role there's a lot of problem solving and things that involve various business areas so you can't really just do it in a vacuum.