SRM can be throttled , special SRM with thrust modulation exists. DRDO working on same
In my twitter timeline have posted on it
There are a lot of articles and research work available on internet for example
Autophage Engines: Toward a Throttleable Solid Motorforum.nasaspaceflight.com
In this study, ground tests of a lab-scale hybrid rocket motor were conducted to verify the feasibility of the hybrid propulsion system for lunar land…www.sciencedirect.comPDF | The SPARTAN research program aims at developing a throttleable propulsion technology, which is mandatorily needed for any planetary soft and... | Find, read and cite all the research you need on ResearchGatewww.researchgate.net
It looks like this stuff is still in the experimental stage though.
The only known experiment done took the heat generated all the way to 3200deg C, that's way too much for something like a CM.
The throttling ability seems to be role-specific.
The new design adds a significant feature. By varying the speed at which the fuel rod is forced into the engine, the thrust can be varied as in a liquid-fuelled rocket.
Being able to throttle a rocket means its thrust can be reduced when reaching "max Q" - the spell of maximum aerodynamic pressure when rising through the atmosphere - and throttled back up again as the air thins.
It speaks of throttling when navigating the different layers of the atmosphere, a problem CMs don't face.
Also, the throttling doesn't seem as dynamic as it's the case with liquid fuel. It appears the throttling happens in phases, as each section of fuel disappears. So it's for a properly planned flight path, where you know exactly where you're launching from, and you know exactly where you need to go, and your comm and support infrastructure is built for that purpose. Otoh, weapons need to be fire and forget. They need to be launched from anywhere at any target that can move, plus can deploy countermeasures. So a CM like Brahmos constantly changes speed, direction and alitude while it travels towards its target.
Also, an autophage eats itself and practically disappears, whereas the next phase of CM capability will require us to bring back most of the missile for reuse. So a Brahmos that flies up to its target, fires off the warhead, and whatever's left returns, thereby functioning like a UCAV. Something that requires a hybrid engine setup that combines a turbojet with a scramjet, so the turbojet can bring the missile home. I don't know how well solid rocket will work with such a setup, probably won't. So I don't see CMs giving up the liquid fuel advantage anytime soon.
For BMs and space rockets, definitely. It's interesting to have the bulk of the body composed of only fuel.