Powerflush, new radiators or both

I am a plumber and have done powerflushing regularly.
Most houses I have done the system works better or has improved efficiency.
Some systems have not been maintained for years and you can tell from flushing what to expect and how well the system should operate after the flush.
All depends on the type of sediments in the system. Brown sludge is ideal thing to flush out the system and you will see a good result. Sediments like heavy scale and rust is a lot harder to remove as the don't break down easily.
But I would recommend the powerflush regardless of installing new radiators or a boiler. My personal opinion I would flush from a firm that specialises in powerflush rather then a average plumber as they should do a better job.
Then I would see how well the system operates after this. If you can get another 10+ years out of the system then I would say thats a good result. Then I would opp to overhaul the whole system new heating including pipes.
As a heating system is like the inside of a person. Over time as the system ages it scales up throughout and reduces flow similar to a human body and clogged arteries reducing blood flow. Heating systems operate the same way and keep spending money on a old system is throwing good money into bad.
This is generally my experience from maintaining old systems as debri is not just in the radiators it will be in the pipes, boiler too.
Another thing is as above make sure to top up inhibitors in the system as these prevents sludge, rust build up in the first place. Ideally top up on every drain down or every few years to keep the concentration to the correct levels.

You can also buy or if your plumber has a thermal imaging camera and it will tell if the radiator has cold spots from sludge. You can take pictures before and after the flush to see the improvement.
(edited)

Take rads off to clean.
Fit magnaclean. That's a magnetic filter.
Run cleaner through system.
Flush
Fill with inhibitor to stop the rust.

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Watch what you do with sludge. I've seen it strip enamel (edited)

Purely observational: if the suspected semi-sludged rads are still capable of raising the room temperature to the required comfort temperature then the efficiency should not be significantly affected, just the time taken to reach the comfort temp may be extended.

with old radiators, it is not value to get a power flush. i would get new radiators.

Had the same thought process last year, so decided to have an extra radiator fitted in a cold area of the house and the Power flush as a couple of very old rads showed symptoms of sludge.
I watched the process being done and for sure a lot of oxide material came out. But, the performance of the old rads has not improved at all, so with hindsight, I think I wasted the money on the Flush and should have just replaced the old rads.

Turn off all rads except the suspect ones and see if they heat up. If they do then it’s a balancing issue or alternatively your CH pump might not be up to the job anymore (ours was under spec’d for size of the house, number of rads).