You can think of the hypergolic fuel as a type of spring. The chemical energy stored in the bonds of the fuel is what pushes the fuel products apart when it reacts. This is what pressure is, it's nothing more than KE of molecules.

The 'spring action' of fuel is very good because there's a lot more energy (per unit mass) stored in the bonds. Orders of magnitude more than a mechanical spring.

But a mechanical spring will reset itself to its natural position once tension is released

Uh, it does - the ‘fuel’ is the other probe.

Notably, this also has a particularly bad ISP?

Also, probes are presumably also heavier and rarer?