Doping

I'd rather not completely abandon the ability for elected politicians to investigate behaviour of those who already have those non-democratically determined honours.

Even if that were a worthwhile thing, there are much bigger crooks than Sir Dave and Sir Brad on the roll of honour. On the very worst possible interpretation of the facts as they are known, they may have been complicit in gaming the TUE rules of WADA in order to take advantage of less canny foreigners in a game of bicycle on the continent. Everybody agreed to the rules and ruling tribunals before the game, and the ruling tribunal says the rules weren't broken. There was no criminality in English law, no British victims of the sleight of hand, and it didn't happen here. Unless you think a select committee should have the powers of god to look into the hearts of men and judge them for their motives rather than their actions, and furthermore that the British parliament should extend its jurisdiction contra mundum in the face of all civilised concepts of territorial sovereignty, then why do you think it's any of their business?

Politicians should investigate the uses to which public money is put, and in the case of subsidising competitive sport they should be very rapidly coming to the conclusion that they should never have let public money go in that direction in the first place and then go after the crooks who let such a thing happen. They are usually conveniently located along the corridor in the house of lords. The criminals here are not the performing dogs, they are the masters who threw them treats.