Actually, you're the mistaken one about that. You're describing a standby UPS, which is the absolute cheapest type and generally only found in the lowest end consumer units.
Most units are line-interactive (which is distinct from double-conversion as they're not floating the battery) and do feed mains through a transformer to step up/down as needed based on input voltage. They only cut over to battery in the event the power drops out completely or the voltage is outside the range of the transformer.
OK, where is that Transformer then

?
I have some 50 Hz 24V 1200V Transformers at Home (bought standalone, NOT in a UPS !), I can tell you you can FEEL how
heavy those Things are: 13 kg each.
1500VA is closer to 17 kg for the Transformer in the same Series that I have.
1200 VA you are probably looking at around 150mm x 150mm x 150mm.
1500 VA you are probably looking at around 175mm x 175mm x 175mm.
Maybe a bit less Iron in the US (although more lossy) since 60Hz, but Still.
I believe you are rather describing an Autotransformer which is a special Type of Transformer with much less Short-Circuit Impedance and no Isolation at all.
Regardless, for a Transformer to vary the Output Voltage, it needs to be adjustable (heh

). Whether it's a Variac (brand Name) where you turn a Knob or whether it's some Brushes run by an electric Motor that moves the Tap Brushes up and down along a Column of Winding (like an On-Load Voltage Transformer / Stabilizer would do), it still needs to be adjustable.
Of course you can do the same with a Power Converter / Inverter (and much more).
You don't get Fixed Output Voltage for a Variable Input Voltage just by Magic of having a "Transformer"

.
EDIT 1: just because of the Size (let alone the Weight), this is NOT something that would fit in a 1U Factor. Sure there are planar transformers for high Frequency Applications, but I believe it would NOT be cost-effective at all for 50/60Hz.