You can adjust your withholding amounts by filing form W-4 with payroll, so that in-year cashflow issue is largely a red herring. (It’s solvable now and would become standardized/automated if the overall system changed.)
Other (more concerning) items you itemize are the real blockers.
In practice, most people do not actually understand how the boxes on W-4 translate into withholding amounts. There'd be a lot of trial and error involved if done manually.
Regardless, there's a reason why I marked that issue as "not a big deal" -- because it isn't -- the other issues I mention are the meat of it.
The issue you appear to have marked as not a big deal is calculating the gross-up that would be required to keep employees whole not the per-paycheck withholding cash flow issue, which you labeled a “real burden” for some (unless I’m misreading your post). I agree both are manageable and would be automated if things switched models.
Other (more concerning) items you itemize are the real blockers.