Jet engines make awesome thrust at low level, due to the huge volume of dense air sucked in by the compressor, which needs a huge amount of fuel to balance the air/fuel combustion ratio. You'd get somewhere real quick, but probably only halfway there due to running out of fuel!!.....you'd also overspeed the airframe big time. Thrust at sea level well exceeds drag.
Jet engines are most efficient operating up at their higher rpm, 90'ish % rpm. Thrust decreases with increasing alt due to less dense air as you mentioned, so there's a nice balance found at high altitude where the thrust at ~90% balances drag to give a comfortable airspeed and mach number.
Unlike a prop, with a jet engine the thrust increases with TAS due to ram effect in the intake.....which can become too fast where you have supersonic air hitting the front compressor (which is bad), so it's slowed down just enough with a diverging intake.
The airframe is then designed around this regime using a lower camber swept wing.............allows high altitude speed with delayed onset of mach induced drag.
The turbo prop hit's a brick wall in terms of efficiency as speed increases. At a standstill the blade cuts the air almost perpendicular to it's direction.....lots of thrust. If you can imagine it now doing 300+kts.....the prop, which will now be very coarse, is cutting the air almost parallel to it's direction....the vector diagram on the prop blade results in less thrust being produced.....up to the brickwall, whereas the jet keeps going hard as it doesn't have this physical limitiation.
Again, the airframe is built to optimise this arena....no sweep, higher aspect ratio.
There's also supersonic mach issues with props at high alt....at tips as you mention.