A lot of these sort of traditions and associations are quite arbitrary really, when you look back at the history.
You'll never walk alone" - I believe this was commonly sung at quite a few clubs back in the 60s, Liverpool ended up "owning" this tradition, but it wasn't really theirs when you go back. I think when that show tune was sung by Gerry & the Pacemakers the association was made stronger. It still slightly annoys me that one, for those reasons. Though City adopted "Blue Moon", and the relevance of "...you saw me standing alone" just makes me chuckle about their stadium!
United wore all red before Liverpool did. I think they used to play in red and white and it was probably Shankly who introduced all red later. United played Real Madrid in 1957 and wore all red at Busby's insistence. As a "practice" we wore that kit against Bolton (I think) in the league.
It might be nice to get "Football Club" back on the badge? But aside from that, what seems to have happened at other clubs is that they're redesigned their crests in the 80s/90s/00s to something sh*t and are now going back to something more classic and timeless, with reference to their history. Ours has been largely unchanged, save for minor variations. The 1968 Manchester Crest is great -it might be fun to reference that somehow with new kits/branding.
I suppose my point is that "branding" has a more legal/formal/corporate feel about it now, going back these things were fairly loose, but when looked back on people seem to feel like they were "always like that". In terms of "branding", I'm still slightly confused why the club seems to barely mention the founding year, 1878? 2018 was the 140th year of United, I'm sure I don't remember much about that?
Personally I'd like us to go back to having more interesting (mad) mascots, in the 30s and 40s we had "Hoppy" Thorne, a bloke with one leg who before games, according to wikipedia ".. would strip off his clothes, down to his running gear, jump over the fence around the playing surface, and hop or run around the pitch, depending on whether he'd attached his false leg or not. Then there was Billy the goat, an actual goat, who actually travelled with the team (really wikipedia?!) in 1905/6 and 1909. He met his end from alcohol poisoning after hitting the celebrations too hard after our 1909 FA Cup win! You couldn't make this stuff up!
I might write to Adidas and suggest our next kit has a badge with a resplendent Billy the Goat, and some kind of "Never forget" or "G.O.A.T" type inspirational phrase added. We've got a brilliant and wonderous history and we might as well have fun referencing it!
Branding now leaves the humourless taste of PR companies and lawyers copyrighting stuff. Didn't Liverpool try and copyright the Liverbird?! Wow, that must annoy the other 50% of football supporters there who support Everton and indeed the vast majority of people who I won't give a monkeys about football! Presumably to clamp down on counterfeit goods? What a shame to deprive people of classics like the 2013/4 Premier League Champions shirts !!