Think you have a different system over there - over here the Tax Disc doesn't prove the car is roadworthy.
You may think it daft, but we have a case here of an insurance company refusing to pay out on a heart attack because "it is the wrong sort of heart attack" - believe me, they will wriggle out of almost anything.
You may take the risk of a $1,000 damage to your car - but what if you hit someone or caused an accident with personal injury - you could be looking at $250,000 - and arguing that the bald tyre had nothing to do with the accident would look a little silly when the Insurance Company has closed its doors on you.
Maybe I am being paranoid - but from the Insurance Company point of view they need to know exactly what they are insuring - stock or modified - and base their premiums on the information you give them.
My wife had an accident in her Peugeot - not serious for either party I am pleased to say - but the assessor was round checking out that our vehicle was exactly what we said it was.
May be different over there of course !