The problem is hearing the downlink. That is why the 19.5" whip is so good. It acts like a 3/4 wave antenna for the UHF downlink and it has almost >7dBi gain above 30 degrees up to over 70 degrees. So it beats a quadrifilar easily (only 4 dBi or so overhead).
As an example, my last four AO-51 passes were 36, 15, 26, and 27 degrees -max- elevation. Would you prefer gain at low to mid elevations, or above 30 degrees to work this satellite today?
A 1/4 wave will work, sometimes, but it is far from ideal for anything but occasional downlink access. As Clayton pointed out, it's easy to spot the guys on crappy antennas, as they are the ones missing calls, or transmitting on top of QSOs, because they mistake a loss of signal as a break in the action.
73, Drew KO4MA
PS My satellite grid addiction started in 2000 with a DR-605 Alinco and a 1/4 wave magmount, and a winter in the Dakotas logging production wells. UO-14, AO-27, and SO-35 were my only breaks from the boredom and snow. Since then I've operated mobile from probably 100+ grids on the FM and SSB birds both. It's addictive.