Your old circuit has a push-pull configuration, which is very inefficient due to the transformer. This incurs a minimum propagation delay through the transformer, which inevitably means power lost through reactive (switching) energy.
No transformer has zero leakage and zero capacitance, so it is unavoidable. One can make a very good transformer, but one cannot eliminate this aspect of the design.
Half bridge is the next best, as it doesn't require a transformer. You still incur the physical length between transistors (and therefore equivalent inductance and capacitance), but this can be much shorter than the windings of a transformer.
When the stray inductance is smaller than the circuit's voltage, current and speed (when expressed as an inductance: 1 H == 1 V.s/A), the circuit will be overdamped, and will not exhibit significant overshoot. In this case, the stray inductance is small enough that it can be ignored.
Because old transistors were limited on speed (perhaps 100 or 200ns switching time), old advice was to minimize inductance, to achieve this condition. Modern transistors are almost never operated so slowly, and therefore this advice is obsolete.
You can still maintain that condition, but be mindful of where it came from, and what the consequences are. Don't just parrot obsolete advice!
The downside to a half-bridge is, it still needs a center-tap. Instead of a transformer (that PP requires), it's the power supply. For an AC application, this is normally a capacitor divider. The load is cap-coupled from the half bridge, to ground (but not just ground as such, but +V as well, for symmetry).
For a DC application (like a class D audio amplifier), a bipolar supply is required.
Or, we can double the circuit, so the load is driven by positive and negative voltages simultaneously. Now the current always flows straight through the supply, with no center tap needed. Downside? Twice the transistors.
The actual amount of silicon required is the same, for a given power level. The half bridge delivers half the (total) supply voltage to the load, so requires twice the current for the same power output. Full bridge delivers full voltage and full current, with the downside that two transistors are connected in series at any given time.
Most power supplies in the 1kW range (which includes your transmitter, as it's nothing more than a switching power supply, with an RF filter on the output, instead of a rectifier) use H-bridge, because the cost of gate drivers is fairly modest, while the bulky coupling capacitors are eliminated (or at least, very reduced). Other considerations (supply bypass capacitors, output transformer, etc.) remain constant.
Tim