I agree, pretty tiresome. But I know plenty regulars that actively find the "songs" to be a bit "wooly" which is a shame.
A bit wooly or a bit shit?
I think part of the problem is people trying to make them up over the internet, never works. Needs to follow the natural evolution in the ale house. A group of mates having a laugh and a sing song and naturally most songs will be shit, and you'll get people saying, "nah, that's wool" (even if it's Scousers singing it). Eventually though someone will come up with something with a decent tune that gets people humming, words will get changed, it'll be sung in the ale house and eventually into the ground.
I think these days people demand a good song immediately and feel it's below them to sing a simple chant until something better comes about.
For a long, long time it was "Only One Micheal Owen" and "Stephen Gerrard clap, clap clap", before anything decent came up. There was plenty of really "wool" songs (that were probably made up by Scousers) for Gerrard until one day a group of lads having a laugh in the pub got it right. And a few years later we came up with another good'n.
As I said, it's still a fairly new team. Nothing wrong with simple chants for new players, regardless of how good they are. Shortly, someone will come up with a second line for Mane's song, pub evolution.