Sorry, this isn't true. The bottom pane doesn't need to be tempered, nor does it need to be thicker. In fact the opposite is true in terms of thickness if you use tempered glass. As well the tank doesn't need to be taken apart to replace the bottom. It can be fixed reliably in in most cases with a patch. The local Big Al's has a 740 gal tank with a patch on the bottom. It has been patched for many years.
You are generally correct, but even though you do not have to take every panel apart, it is still a major undertaking to remove/replace the bottom plate, even more so if there is a frame attached....
so let's just say we are both right.
It also really depends on where, how long, and what direction of the crack as to whether or not a patch will hold.
If it is a crack in a corner or something, sure I can see a patch working, but if the crack bisects the middle portion of the plate, I simply wouldn't risk it failing.
Also an incomplete crack will continue to run, putting a patch on it will do absolutely nothing to prevent that. The only way to fix it is to go through the trouble of drilling the crack, patching it, etc. like is done with car windshields, only problem is most tanks use tempered glass for the bottom and tempered can't be drilled, at least not by most hobbyist.
Not knowing the specifics of the tank in question, I opted for giving the "safe" answer.
If it were a 740 gallon tank then the impetus too patch it would be considerably greater, but a 40-50 gallon tank can be had anywhere and rather inexpensively.
Whenever you consider things like craigs list, Petco $1-a-gallon sales, etc., etc. and how much the OP's time is worth, it quickly becomes easy to see that in the long run it would be cheaper and safer to simply purchase another tank.