I would take a lot of that with a hefty pinch of salt - there is case law that means that insurance can not be refused unless the reason is directly relevant to the claim - so no declared towbar as above, no insurance for towbar or trailer is reasonable - but no declared towbar and the car is hit by lightning - irrelevant and therefore they must pay out. The other let-out clause for the insurance company is if they can show that they would not have offered insurance for a car with that modification at the point of insurance - e.g. you insure a 1.0 polo and put a 5.0 v8 engine in it - most insurance companies could show that they would not have insured that car, and therefore even if hit by lightning (i.e. engine is irrelevant) they could choose to not pay out.
comment above about type of tyres is a red herring - if they are the correct size / profile etc. for your car and within manufacturer specifications for speed ratings / load carrying then you are fine - there is no basis on which an insurance company could refuse a claim - same for what fuel you put in / type of windscreen wipers you use / type of brake pads / etc. - all consumables and as long as you buy replacements suitable for your car and which are road legal you are fine...
my best experience with modifications was when insured on a range rover years ago and some road debris punched a hole through the oil filter at speed - engine went from running to solid in seconds! The insurance company sent out an engineer, they specified an engine rebuild which when done took the engine from 4.2 litres to c. 5.0 litres - all to their instruction... A couple of years later (so having renewed in-between)
- sorry sir, we can't renew this car it has an engine modification and we don't insure modified engines
- but you specified the modification and have renewed insurance since...
- sorry sir, computer says no - we have never insured modified engines...
- but... but... oh well...
Too fast / too slow is too simplistic
the reality is that an accident on a bend where you are going at 70 in a 60 they will most likely pay out - doing 150 in a 30 / doughnuts / drifting / etc. probably not. As for too slow - would love to see a refused claim on that basis - how do you define too slow - other than on a motorway where there is an expectation around driving with the flow of the traffic there is almost no chance of ever being prosecuted for 'too slow' otherwise how do you slow down and stop!
fronting / business use / any other reason where you have lied to the insurance company - sure, it is fraud.
tinted windows - again, they would have to prove that the windows were material in causing the claim
so, soundbites without proper research...
generally speaking most people will never be in that situation - most people buy a car and drive it - they are honest in declarations when applying for insurance and they are not stupid in how they drive...