The trial is intended to let people try Spine before purchase. You can explore the example projects, try out all the functionality, and make sure it runs on your specific computer. For those goals it doesn't need save functionality.
We never intended for people to do actual work on the trial. Not being able to save is a pretty clear signal for users that that is the case. However, you do have a great point that making it easier for people to learn the software would be beneficial.
Currently you can learn using the trial, though as you mentioned working across multiple days would require to leave Spine running during that time. That is actually a pretty reasonable workaround, though if Spine crashes, you'd lose your work. Good thing Spine very rarely crashes!
Another idea is to run the Spine trial in a VM, like Virtual Box (it's free). You can save the VM state, shutdown your computer, and resume the VM state later. Of course a built-in solution would be better than any workaround, but maybe these ideas help.
One issue with allowing the trial to save is that 100 people could do work using the trial without a license, then use only 1 license to do exports. There may be ways around this, like prevent a trial project from being opened by the full version. However, the problem remains that the trial isn't for doing real work. I guarantee many users would be upset when they work for weeks in the trial, purchase, and then can't open their trial projects. People are already upset that they did work in a single trial session and they can't save it.
There may be a solution where a new Spine license could open trial projects only for the first week after purchase, or something like that. That could likely work, but it's pretty complex. We are a small team and we have big dreams for super cool new features. We want to get those done so people can use them and honestly it's hard to put that aside to find time to work on a complex trial project saving mechanism.
We are open to any other ideas to make it easier to learn Spine!