There is no technical barrier to a Apollo style Mars mission, and has not been since Skylab/Mir, with a well math'd Venus flyby proposed for 1973 that had answers for most of the points in the question.
The issue is this mission design is very much brute force - launch a large craft and then stuff it with several years worth of food for a very small (2-3 person) crew, that crew does as little as possible while in transit (reducing life support needs). If possible provide a lander so at Mars crew can plant a flag rather than just looking from orbit, then fly home.
The most costly/risky part of this mission is the lander, which is outside the human factors scope of the question.
The issue with the above mission profile is 'why'. It achieves a very expensive 'first' but otherwise is mostly about astronauts struggling with boredom and pooping in a bag which is hard to justify to taxpayers (and probably the crew).
An obvious improvement is to make life support more closed loop:
- Lower launch mass/cost (in a way clearly explainable to the taxpayer)
- Allows (and may even require) larger crew size (can bring actual geologists etc to Mars, rather than giving an astronaut a crash course)
- Much more 'going on' both for crew and public interest
- Design and possible even vehicle itself re-usable.
- Lots more 'what do we do next' mission options.
Issue is that this makes mission much more complicated, and in particular there is three axis problem space of maximizing closed loop efficiency, reducing system mass and maximizing system reliability that while certainly solvable tends to produce decision paralysis in full system design in absence of firm mission scope and budget, while plenty of work has been done at subsystem level.
This means that should someone NEED to pull together a Mars mission 'by the end of the decade' most of the life support parts are already there, they just need to commit to choices and start iterating on hardware (ie spending money in large amounts).
So it could be argued the biggest obstacle is right combination of money and willingness to lock in a choice that is 'wrong' by at least one metric.