I was wondering whether solid tyres would be more likely to deform alloy rims during impacts than pneumatic tyres?

Absolutely - for a road bike, notwithstanding "vertically compliant" frames and other sales nonsense, that ~1" of compressed air between the rim and the asphalt is the sole suspension component for 150-200 lb of combined rider and bike weight. Remove that, and every bump or pothole is transmitted directly to the bike and rider, and of all the parts, the rims and spokes are likely to take the brunt, located as they are between the ground and the rider (i.e., the heaviest part of the equation)

I rode with "No-Mor-Flats" tubes for a couple years on my mountain bike (I got fed up with finding anywhere from 25 to 187 goats head thorns in both my flat tires. For some reason, the rear always had more ... And, yes, I did count them.) and never had a problem with the rims or spokes.

Airless tires or tubes do weigh considerably more than a pneumatic tube and tire, so that may be something you'll want to take into consideration.

On my mountain bike (1984 Fuji Mt. Fuji) it felt like the airless tubes nearly doubled the weight of the bike when I picked it up.
The added weight did not bother me while riding, nor did the additional rotational weight.
I did go back to pneumatic tubes, a few months before that bike was stolen.

I think it is Green Tire that makes airless tires you can have custom made to a density that will "give" the same amount as a pneumatic tire at whatever air pressure you want, at no additional cost.

Hm - clearly I need to educate myself on the distinction between "solid" vs "airless" tires before spouting off. Disregard everyone I said!

I'm happy that I came across this tread as the fact that ' solid tyres would be more likely to deform alloy rims' was an axiom for me. I dunno how this idea came to my mind though...
Well, seems like today I learned something new.

"Solid" inserts are quite different beasts. Clincher tires rely on parts of the bead being able to fit/slip into the deepest section of the rim to get the last bit of the bead over the edge of the rim. With pneumatics, no big deal. But with "solid" inserts, the bead needs to be PULLED under the insert to free up enough bead to allow the tire to be mounted. This leads to a not always happy compromise between firmness, tire fill and the ability to mount the tire with reasonable force.
For mtb/hybrid widths, sure. Once you get to road bike widths, the equation changes. Far less volume there. Once you consider that you won't need the flat-fixing stuff anymore, the weight penalty is pretty much gone.

Wasn't a big deal for me either.
Yeah, or at least did. That's where I got mine. Extra firm.

One thing to consider, particularly with the greentyre brand, and probably with all polyurethane tires/inserts, is that they change firmness with temperature. Mine (extra firm) rode OK in 3 seasons. But below freezing, it felt like riding with a fan belt wrapped around the rim.

That might still be true. They will transmit impact force more directly to the rim. But something being true doesn't guarantee that it's important. I used a good-quality double wall rim and didn't have any issues with flat-spotting or flared brake tracks despite riding with a pannier for thousands of miles.

It gets down to how particular you are about the use of language. Most "solid" tires are actually kinda-sorta foam. Slice them open and you don't get a shiny surface, you get loads of tiny, tiny bubbles.
Airless, airfree, solid, I don't particularly care. I'll understand. We talk about tires or inserts that don't need to be inflated and don't rely on some sort of spring action.

The pros and cons for various kinds of use is far more interesting to talk about.