So you're improving a circuit with "too many components" by making it worse, then adding more components to fix it?
The most important part of the circuit is having it not be the god damned 2N3055 POS that everyone else on the internet jumps to.
After that, yes it could still use improvement, but it's a better "getting started" circuit, at least.
If you check the range of duty cycle available with the resistors and pot shown, you will see it won't burn the transistor. Assuming the FBT is doing its job, of course -- a circuit with a UC3842, say, is always safer, but takes more stuff, and probably not as likely to be on hand as a 555.
Likewise, the RC is there to absorb some ringing, and doesn't get hot. Obviously, if it's burning, use a bigger resistor (or just forget it altogether, it's not important). The 22 ohm 1W I would've thought would be a bigger offender, especially with the 2N4403 being practically in hFE limit.
The chain of 1k resistors is necessary, if you study the V_OH and V_OL of the 555 and the transistor Vbes. Actually the top resistors should be smaller, for the aforementioned reason.
MOSFETs are good (and can... kinda sorta, be direct driven from the 555, but it's not as good as with a proper drive circuit), but the high voltage required (>800V) sucks for most purposes. You only find those in newer flyback/forward PSUs, and even then, none over 1kV. And those over 1kV suck on Rds(on), to the point where the BJT is actually starting to look better for performance reasons, despite its drive difficulty and slow speed.
It's noteworthy that my Trinitron has a MOSFET powering the high voltage (the FBT -- but not the HOT, which is a massive 40A BJT), but again, being that's high-falootin' equipment, they could afford to do that.
Tim