NS it doesn't seem unreasonable to me to reinforce the rule by giving ATC a role. They already do for aircraft landing at or departing from airports in CAS, and for aircraft transiting the London CTR through the Heathrow overhead.
No they don't. Mats Part 1 Sec3 CH1 P7 Para 9.4.1 - 9.4.3 covers it.
Whilst that specifically covers aerodrome operating minima the same applies for flight rules, they are in simple terms the aircraft commanders/pilots responsibility to adhere to them. If ATC are to 'police' as you say then your perfect storm is three or four aircraft on approach travelling at three miles a minute, all non native language speakers, being questioned as to their operating procedures and capabilities. A very quick way to an accident or incident, due to misunderstanding/overload which is part of why absolute minima procedures within MAts Pt1 changed significantly in 2012, to those outlined above.
The crew know what they and the aircraft are capable of, its up to them to ensure they stay within the rules, or operate outside them for very good reasons.