DT-I am curious as to why you ask?
Anyway I doubt If you will find anyone flying fare paying punters who would even consider it.The best I have been able to do was in a modified BAe J41 into London City max at 7nm 4,200 aal.Even then we had to intercept the glideslope fully configured to land at minimum approach speed;10 knots fast = go around as you could not get the speed off.
In my Emb 145 a ROD >3,100' is more than three times what I could accept for an approach,several reasons.
1 Not enough drag producing devices to prevent rapid increase in speed,beyond flap limiting speed.
2 Engines would have to be at flight idle and the spool up time would prevent a safe go around from anywhere below 500'
3 GPWS would pop it's circuit breaker as it wanted to tell you terrain,pull up,sink rate and glideslope from 2,000' onwards.
4 Even upper air you dont exceed 3,000'/min as the pressurisation system can't restrict the cabin rate of change to less than 650'/min.
5 Most importantly,in a swept wing a/c this would be little more than a controlled crash.The angle of attack required to arrest such a descent would be horrific.The only time you are going to use this kind of landing technique is if you all your engines quit.