Are Helicopters allowed near busy airports or any airports at all and if not why not
Yes, helicopters are allowed near busy (and any other) airports, because why not?
Ok, seriously: helicopters in general are just as able aircraft as ones with fixed wings. General limitations for use of airspace may be in effect depending on airspace categories around aiports, but to my knowledge there are no airports in the world that would specifially prohibit operation of helicopters in their airspace.
Some private airfields may have restrictions for helicopters and other aircraft due to noise, but I'm guessing this is not what you are asking?