The system itself isn't asymmetric.
You can't say that without knowing exactly which transmission standard is being talked about. Some of them are inherently asymmetric, some aren't.
The first 1 Gb/s fibre to the home standard was multi-drop, I can't remember the standard number off the top of my head, and had an inherently asymmetric character - it was, rather foolishly IMHO, baked into the scheme used. It used a statistically multiplexed broadcast downstream (i.e. diversity) and a time division multiplexed upstream. So, if no one else was using it you could get the full 1 Gb/s downstream, but you were limited to your timeslot for the upstream, something like 10 - 25 Mb/s depending on quite how many stations were on a single fibre loop.
That standard didn't get much of an uptake and I suspect it was because even the telcos realised that it was a compromise too far and would be too limiting before its natural replacement time came around, even though it was comparatively cheap. The cost, after all, is in all the digging*, not the fibre itself, and it's foolish to go for a standard that has minimising fibre usage at its heart and encourages you to lay a very inflexible multi-drop fibre structure that won't likely be useful for future schemes.
Most of the FTTH/FTTP that's being rolled out now uses some form of passive optical network that's essentially a cut-down version of the wavelength division multiplexing that's been around on the 'big boy's kit' for more than 20 years.
*Back when I used to actually have to worry about paying for this stuff, it cost about £500 a metre to bury a duct under a metalled road, about £100 a metre in a soft verge. The few pounds a metre for the actual fibre is almost noise against those figures.