If you look at this link to the 1890 OS map
http://www.old-maps.co.uk/Map1Enlarge.aspx
you can see that it seems, as you originally thought, that these are older rights of way that had to be respected by the builders. Daisy Bank crescent appears to have been built inside a land plot defined to the east by a lane that runs from Gillity Greaves to Sutton Road, and this lane is now part of the fottpath network you have noticed.
Judging from the lack of chimneys on google earth, the houses to the east of this back lane were built some time after the daisy bank ones - the back lane would have been part of the boundary defining the newer housing estate.
You can also see how the lane system further east was used as a parliamentary boundary - if you dig deep enough in the records, you may even find that this is a very ancient boundary going back to Saxon times. I'm not saying it is, but it is sometimes the case, that older manorial or burgh boundaries simply carried on in the landscape.
Have fun with the old-maps website - what is intriguing about these footpaths is that they seem to have existed before the canal, as many of them run over the canal on footbridges.
If the spirit moves you, there should also be a rights of way officer at your town hall who can help you with queries about footpaths.
What an interesting area you live in!