Every answer has some key points as to why airliners today SHOULDN'T have conventional landing gear... but it could be done despite the angle of the aircraft while on the ground (for loading/unloading cargo/passengers) or the drag, or the forward visibility while taxiing, or prop clearance (which wouldn't matter if we're talking about modern jet airliner designs)...
Putting aside safety concerns (prop clearance, stability, etc.) Comfort, loading and unloading concerns, practicality, expenses... Only focusing on why a modern airliner can't have a conventional landing gear... there is no physical reason, to my knowledge, as to why a modern airliner can't be configured as a tail-dragger.
The biggest reason why a modern airliner SHOULDN'T be configured this way... (which is a completely different question than why it CAN'T) would have to be the fact that the jet engines would need to be inline with the fuselage which means that until the tail of the aircraft generates enough lift to raise the tail (making the aircraft level with the ground) the jet engines thrust would be directed towards the ground and with jet engines becoming more and more powerful, this could cause a lot of damage to airport infrastructure and the aircraft itself and would put ground crews in an even more "danger close" proximity to the jet blast...
I'd also venture to say that it may become pretty unstable before it could reach rotation speeds (V1), and I have to wonder how the jet engines would effect the rest of the aircraft when they are spooled up to full power while the tail is still on the ground... I can imagine the engines wanting to stress the engine mounts to the point of some sort of failure whether the engines detach completely or twist the frame of the wings and/or fuselage, maybe even make the aircraft jump off of the ground or even flipping it over and in any case... causing the aircraft to become incapable of sustaining stable flight.
These factors, and more, make a conventional gear configuration completely invalid for a modern airliner. It could be done with enough capital for research and development that would have to change every preexisting design concept to date... reinventing the modern airliner to be something entirely different all together if it were to ever see flight while maintaining the standards and requirements (safety, performance, efficiency, production and operating costs... etc.) that our existing airliners must meet before being put on the market while being cost effective.
Thanks for reading!