Many, if not all, FM broadcast stations in the US transmit both a
vertically
and horizontally polarized signal. So, rotating the antenna 45 degrees is
not giving up anything.

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Simultaneous transmission of vertical and and horizontal polarised signals
from a single antenna system is impossible without upsetting the desired
radiation coverage pattern.

What you mean is your clever US broadcasting engineers have designed
antennas which radiate "Circularly Polarised" signals.

As Cecil says, nobody gains anything power-wise. For the same transmitter
radiated power everybody's signals are 3 dB down (half-power) relative to
simple linear polarision when both transmitting and receiving antennas have
the same polarisation.

The advantage of circular polarisation is that it doesn't matter which
polarisation your antenna is orientated because, in practice, when erecting
it, the polarisation received by your antenna is usually a matter of
guesswork anyway.

Only with relatively-rare, direct line-of-sight broadcasting propagation is
there any certainty in the polarisation of received signals.
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Reg.