My thoughts (above) as well.
Have had an off/on relationship with fixed all my life. My first was a Hill Special, my 10th birthday present! Never knew anything but fixed for a few years. Then I left it outside Woolies in Prescot and it was nicked. For a while I managed with a bike donated by a neighbour, until I was 14, then got the bates you see in my avatar pic. This had gears and was the first bike I raced on. 26" wheels, steel handle bars and chain set, yet still managed a "6". I swapped this for an RJ Quinn, with sprints and alloy chain set, but took me months before I went any faster.
I then picked up 2nd hand Mercian track frame, from a well known rider in the mid Shropshire whlrs. But, strapped a simplex rear and had a single 54 on the front. I think my bottom gear was 81" !
Did quite well on this hybrid, even rode the IOM 1 lapper on it.
I tried a couple of times riding this bike as a pure fixed m/c, but I seemed to go slower.
The Mercian, then got dismantled and went in the loft as I rode several geared bikes. But I never matched those times I did on the Mercian/gears combo. Years later, I'd got back into racing, but I only had the one bike, which was not dedicated to racing, so I got the Mercian down and had it resprayed, bought a cheap pair of wheels, one brake and some aero bars and used it for racing. It was a delight to have a clean bike just for racing. I found as well that it was quite consistent in my times, matching some of middle years when I rode gears.
Over the last 5 years, I've upgraded everything, new wheels, frame (a Nelson track) and continue to put in some good times. Managed a 25min 10 a few years ago, almost 40 years after my 23min PB. I've gone a bit slower the last few years, but breaking collar bones now and again seems to have that affect!
But at the back of my mind, I always think that gears should be quicker. So every now and again, I use my gears bike, similarly equipped, but I never achieve anything much different and usually 30secs slower.
This season, I am preparing a fixed and a gears bike. Not a top end bike, but similar and I hope to answer that question - "which is faster - gears or fixed" once and for all.
But for anybody starting to race, a dedicated fixed bike, with aero bars and good tyres, is a very cheap way of getting into time trials and on the short courses (10 & 25 miles) very competitive. Your times won't be much different from a bike costing 2 grand more.
My first race should be in a few weeks and then I'll start the gears/fixed experiment again.
Cheers keith