This has come up a couple times before (Algebraic sovler problems (Laplace approximation in Stan) [this is @anon75146577] , Is it possible to access the iteration/step number inside a Stan program?) for people who are solving optimization problems in Stan. I guess add to that list any use of the algebraic solver as well.
You want to use a good guess so your optimization runs quickly, and the natural good guess in this situation is the last solution you found. In the 2nd thread above Bgoodrich points out you can hack this in with some C++ and memory storage.
I don’t know for sure, but my guess is this is very important.
Lemme quickly point out that these optimizations are done every leapfrog step, so you really do expect your last solution to be reasonably close to your next one (it’s not going to be as big a difference as the solutions between different draws).
It’s going to be easier to change Stan Math to work with math than expecting math itself to adapt to the limitations of Stan Math :P. Bring it up in a meeting (or make an issue or a Discourse post) and get it on the problem radar