The question as to whether or not it would be better to replace the tree or to try to nurture it is really difficult to answer without more information. How much has it grown over the period of time that you've been there would be helpful to know. What type of soil is it in (where do you live)? How old would you guess it is?
I'm assuming that the damaged area of the trunk has already fully healed, so applying tree trunk goop is probably not going to help matters. If it's not healed then goop will help speed that up. The best thing that you can do is to improve the health of the tree and give it the best opportunity to recover.
Ensure that the root flare is exposed. The trunk should show a flare where it inters the ground. If it goes straight into the ground like a telephone pole then the tree is too low. Excavate soil, gently, until the flare is exposed if necessary.
Make sure that there aren't any girdling roots. If there are any, then you need to carefully cut them back away from the trunk. Do NOT rip the cut root out of the soil since it will damage other healthy roots. If there are many of them then do a couple of the worst ones initially and leave the rest for next year.
Apply the full sick tree treatment as outlined at the top of this forum.
Others here might have some other suggestions as well. Good luck with your sweet gum and let us know how it goes!
~Dave