Nut,
Actually, it did. It was called a very large engine with an oversized front fan. It also carried a lot of additional structural weight to locate the engine in the middle of the fuselage.
There were other penalties, but these were overcome by brilliant design and detailed engineering so as to make it a viable combat aircraft.
You might also note that the F-35B's lift system is used for STO as well as vertical landing, slightly useful if you want to operate from a ship, or short runways.
The point I'm trying to illustrate is that getting a powered lift aircraft to work well enough to be an effective military combat jet is 'crazy hard'. It always involves compromises, clever engineering and significant risk. The Harrier was the only successful one of many attempts to develop such an aircraft - my opinion (and that's all it is) is that the F-35B will be the next. Many think it won't - that's fine too.
Hope this helps, best regards as ever to those making function meet requirement
Engines