AC power is like a trusty work-horse. DC is like a rhinoceros.
AC power is easy to manage because it reverses polarity 100 times a second, which means you have a zero-crossing for voltage and a zero-crossing for current (not necessarily at the same time). This means AC arcs tend to self-extinguish, and switching hardware has an easy time of it.
Higher voltage DC power has no zero-crossings. Thus, once an arc begins, it cannot be reasoned with, it does not know pity or remorse or fear and absolutely will not stop, ever, until your entire machine is magic smoke.
That was 600V. 230VAC will rectify into 325VAC, more than half that.
It won't make a hill-of-beans difference in heat
Rectified bouncy-ball DC is exactly the same power as regular old AC. As dandavis mentions, you would lose a tiny bit in diodes and devices (but then, heat is your objective).
Making it DC doesn't make it more controllable
As discussed, less controllable. You're thinking "MOSFET" because that's the tech you're familiar with. But AC has its own tech that's just as good if not better -- the triac.
Look at any random $12 AC light dimmer. It is a triac. This is extremely simple and cheap because the triac doesn't need to interrupt AC power - the AC zero crossing will switch the triac off automatically.
The dimmer only turns the triac on.
Since a power half-cycle is 10ms (8.33 in 60Hz land), you can simply wait n milliseconds from zero to turn the triac on, with "n" being the variable. It's not linear - you must think of the power content underneath the sinewave - but it's easy.
Of course, this degrades your power factor, so you may want to think about that.