There probably are too many entries in that log to give a longer log or full log. It would become too large to store and it isn't required to have.

Too large to store? These are text strings...

this is a good idea but the modlog would take a while to load

Yes, even if just a couple of users find it useful, it would still make sense to make it available.

Isn't the full modlog stored somewhere offline?

I think that the problem is the resources to make a search in a giant modlog with years of entries, more than the size itself.

And in some decades the size may be a problem too if many people decide to download it(bandwidth problem instead of storage problem)

I don't think the problem is with the capability to make it available; the issue is whether giving access is correct necessary.
I expected one of the mods to reply to this thread.