Jim,
Two things I will comment on.
First, there is no such thing as "First come, first served" any more at busy airports. It's "Most efficient", which basically means the most planes in the least time. The Sentence in the 7110.65 says:
Provide air traffic control service to aircraft on a "first come, first served" basis as circumstances permit, except the following:
As you noted, a Piper Cub on a 10 mile final could seriously disrupt the flow of biz-jets into an airport, so does a Cherokee, and even an old Citation. It's just a matter of degree. I understand your frustration at being moved out of line when you were doing 120 kts. I can recall being vectored off the final
repeatedly at busy airports in the '70s while flying a Beech Sierra at
Full Throttle .
It isn't a new phenomenon.
Put another way, you're 5 out doing 110-120 kts, so the fellow behind needs to be about 5 behind you doing 145 kts, and the fellow behind him therefore needs to be 5 more miles out doing 170, and the fellow behind
Him needs to be another 5 miles out doing 200 kts or so. So now you have a 20 mile final that's only got four airplanes on it. This to allow for "compression" as the aircraft nearing the runway must eventually slow down to land. (We try real hard not to have jets doing Vref 20 miles out, as the howls of protest get quite loud, rightly so.)
Jim, you cannot
Survive working a busy finals position with limited airspace if you can only get FOUR aircraft on a 20 mile final, though such a sequence might work just fine during slower periods.
Then there are some other factors which come into play, such as airport layout, (are they using closely-spaced parallels, same runway for departures, or another, etc.) Winds, and whether visual or instrument approaches are in use. Just yesterday, I was working ILS approaches with 25 kt headwinds at the surface. Compute the spacing required when a Cherokee is only doing
60 KNOTS groundspeed from 7 miles out. (that's SEVEN minutes + to land and clear the runway) It's ugly. It happened several times yesterday. And don't forget, in the exact same conditions, you're being fed arrivals on downwind that are doing 280 kts over the ground. (210 kts IAS corrected for TAS and tailwinds, plus a nominal cockpit "fudge factor".)
The second thought I want to leave you with is that South Florida is at the
PEAK of it's travel season, and the last week we've gotten almost daily flow control restrictions to FLL, among others. So some of those "Fat Cat" biz-jets that passed you on your 5-10 minute vector delay had in fact been delayed by an
HOUR or more on the ground at their departure airport before takeoff. That's not a joke, I worked the Tower last Thursday, and some of the delays to FLL were that long.
I hope you don't take this as a "flame" directed at you personally. I'm just trying to explain "our side" of the picture.