I tried the same practice in a C172, flying over a disused airfield at 3000ft at less than half a mile out. With 40deg flaps, no throttle, and 75-80 knots the C172 made it onto the glideslope with room to spare. (note. Max Vflaps is 85knots, and no side-slips are allowed with C172s.)
1/2 mile out =2640'
You are at 3,000
Even 60 MPH only gives you 30 seconds to reach the threshold from 1/2 mile out.
ROD 6,000'/min.
Must have been a good day!