I kinda agree with the point of your post - Pulsejets represent the sort of redneck engineering, that no self-respecting aerospace engineer would've considered before the Ukraine war. And aerospace companies aren't too keen on delivering weapons that can fill the niche of their high-end cruise missiles at 1/20th of the cost. But the recent war has proven that drones built out of DSLRs, scooter engines, and $200 worth of smartphone parts and hobby electronic supplies combined with cold-war surplus hand grenades or RPGs present a real and present danger to even modern systems.
All the arguments mentioned about the lack of stealth would be countered by their speed and inexpensive nature, once again creating a huge dilemma of shooting them down economically.
That being said, I'm doing armchair engineering here, and there might be perfectly legitimate reasons why this would be a silly idea.
Checking on Aliexpress, for the $5k, even 50lbs is kinda ambitious, and I feel like you'd need more (the Tomahawk has 600lbs thrust ,the Storm Shadow has twice that).
Just to make my point, lets compare a Storm Shadow, to the V1, a 80+ year old design (V1 vs Storm Shadow).
en.wikipedia.org
en.wikipedia.org
Speed: 400 mph vs 700 mph
Range: 160 mi vs 310 mi
Payload: 850kg vs 450kg
Please keep in mind the Storm Shadow is air launched while the V1 isn't.
Even such lopsided comparison against my idea shows that it has potential. A modern V-1 equivalent with GPS guidance, optical target recognition, etc. (these are features available on inexpensive drones) with half the payload (due to increased accuracy), would be a dangerous weapon indeed.
Not sure if it makes sense to air-launch it, but if it does, it would probably close the performance gap even further.
Also please keep in mind, the Storm Shadow's max range is determined by the INF treaty that limits its range to 500km (310 mi).