You certainly should keep it. Even if you don't use it for a while - maybe some time in the future you will figure out a use for it and figure out a way to use it. You have a 10x28 lathe, I can imagine that it would be quite useful for quickly opening up holes to get a decent size boring bar in. I advise that you get set up for tool post drilling (don't try to push a drill bit like that from the tailstock).
I had a couple large rough drill bits (both 1-1/4") that came to me as scrap. Following many of the suggestions above (and a few of my own), they are now both in good condition. They are now perhaps the most expensive 1.25" drill bits anyone has ever seen!
The first one had a MT4 sleeve welded on (crooked), and with the weld metal and rough grinding on the morse taper there was no chance at all of it holding. I straightened it and recut the taper. I actually used a lathe about the same size as yours for the machining (11" swing) because it has a nice taper attachment (gave me an excuse to use the TTA). I made a split sleeve (without the sleeve the jaws would not land evenly) and held it in the 4 jaw chuck. The first operation was to carefully make a tiny spot face and center drill the outer end. Even with getting it pretty straight (which was a pretty arbitrary shot, since the previous owner (the guy who welded it?) got it crooked and offset) - I had to take quite a bit off to get it to clean up. Remember that taking just a little off the diameter pushes the taper up quite a ways. Anyhow, the taper carried into the flutes of the drill. As you probably know, the shank of a HSS drill bit is easy to machine, but the flutes are full hard - which made for interesting machining (used two edges of an insert), with the chips coming off as very tiny blue curles. Then recut the tang. My mill is set up with an MT4 adapter.
The second one was more challenging. It had a MT3 sleeve welded on. It was just bent and the bearing lands near the tip had been chewed back (pretty common issue). The tip was easy to address, simply cut it off with an abrasive chop saw and repoint. The straightening gave me a lot of trouble. The method I use is to map the bend, then clamp it straight on a big piece of square bar and heat it at the point I want to bend it - let it cool. After about 10 tries, I could see the previous weld was cracked. So I dug out the crack, welded it up (several times), more straightening - got it pretty good, then reground the taper (excuse to try out the T&C grinder, again I held it over a sleeve) and cut the tang. I have an MT3 holder for the tool post.
I'm very happy with the results. You should fix it up. It is a challenge, but once you get at it I think you'll find it is not really a big deal. Let us know how you make out. Regards, David