Problems? You came to the right man!
-Cars. Not just the legally driven ones which are abundant in my area resulting in huge traffic jams, but also the ones driven by people illegaly, whithout any concern for the law or the safety of cyclists. Illegal double parking which makes you ride in the middle of the road as well as passing red traffic lights comes to mind.
-Unsafe roads. Missing gutter covers. Lots of trash on the streets.
-Low visibility on the night on various parts. Especially dangerous in the night when its raining where that small pool of water can be as 10cm deep and you dont know if its safe to go over it.
-The problems you mentioned above. Its really hard to find a safe place to ride. Unless you go through some pretty bad parts to go outside the city to a country road.
-The bikes are nowdays pretty good, but some of them are overpriced IMO. So are some parts and gear. Carbon fiber is not an expensive material and I dont believe its costly to make a CF bike in terms of energy requirments etc... Unless R&D costs that much... Which I doubt...
-Lack of cycling lanes and parked cars on cycling lates. Garbage cans are often placed on the cycling lanes.
-As far as the "sport" aspect of it... Unless you live in a nice clean city, with clean air, nice roads etc... its a bit miserable to go cycling for exercise in the road traffic with all the above mentioned problems.
-Doping and overtraining makes it no longer "fun" to train for events...
-Bike theft, allthough the law does consider the bicycle a "vehicle" it does not issue traffic plates for them, making bike stealing extremely safe and easy for the thieves. The more you spend for a bike... The heavier the lock you need gets... Mine at the moment is a hunk of metal about 3 kg and they -still- tried to pick that when I left my bike outside the gym once.
and a few others...