I really enjoyed the Ash and Gary's friendship and their Johto League battle is still one of my favorites of all time. Their dynamic was just antagonistic enough witohut it going overboard. Like others stated, the fact that respect came long before their final battle helped out. Plus I liked how Gary, even after dropping being an active trainer still could hold his own against Ash and still pushed (his battle frontier appearances were the best post-OS for me). I really wished that he could have been shown more after DP. I feel like he could have at least made an appearance in Sun/Moon and definitely in the new series.
I do agree wtih sentiments that the rivalry was underdeveloped a bit. Nowadays, the one thing that I prefer the Ash/Paul rivalry over the Ash/Gary one was the sheer amount of appearances and confrontations they had. I feel like we could have seen more battles between Ash and Gary prior to the final bout to build up more suspense. Also, it would be nice if he made more appearances so we could get a less rushed backstory between them.
And honestly, and Ash/Gary travelling around for the new series would be super interesting. I actually don't mind Gou as a character but I would be more invested in watching if it was Ash/Gary. Who knows maybe Ash and Gary (with Go) might get a small arc to travel around. It would be great to see the dynamic and it would be low key hilarious if Gou got jealous of Ash and Gary's friendship (considering Gou has a hard time making friends and Ash has such a strong dynamic with Gary that has a long history).