I couldn't stop laughing while reading this thread.
Very interesting debate!
Are Timon and Pumbaa really important? I would enjoy TLK less if I didn't have Hakunamatata. Having such characters that are outgoing and are able to create a careless atmosphere is super important to the movie. Simba seemingly forgets about his past and troubles because of these two. They left him no room to ponder. But even though he was having a fun time with Timon and Pumbaa, his troubled past stayed with him. This makes the good message that simply ignoring fears doesn't fix them; And what better way to ignore troubles than with Timon and Pumbaa.
I would have to agree that it didn't have to be Timon and Pumbaa specifically. They could have been some other characters but had to fill in their roles. Nonetheless, I think having Timon and Pumbaa was a very creative decision. I feel like they add variety to the movie meant for family watching.