The simple explanation, that you probably didn't require, first - a large proportion of the flight would have to be super-sonic for the speed to significantly affect journey time. A flight that was as much take-off, climb, decent and landing as it was actual flight, would gain not much if anything.
The current crop of standard medium-large civil aircraft engines (high by-pass turbo-fans) are burning something like 20% less fuel than the equivalent engines of 20-30 years ago, for a whole raft of reasons in terms of design although they boil down to running hotter in the combustion chamber and turbines, and working at higher compression ratios. (That does nothing to offset the VAST increases in air travel however.)
Flying very high, air resistance is less, so requires less energy - that is simple maths, although you do have to get there and back and be able to actually fly in very thin air.
I have just seen that, very oddly, they are looking to use an ancient, very simple single shaft GE engine, most commonly used (as a variant with an after-burner) in military planes. That would make you think that fuel economy/emissions would be pretty horrible. Presumably the problem is one of cost for developing a new engine from scratch???? Educated guess for a new engine - $100,000,000???? More????