I have heard that notion before, but don't know how the maths is supposed to work.

I can tell you, though, that light would be going faster than light, if it could.

Here's a simple equation you probably know:
F = m * a
(F is force, m is mass, a is acceleration)

Well, if you rearrange it, you get this:
a = F / m

We currently believe photons to have no mass.
Insert that into the equation and you get a division by zero, but our closest approximation means acceleration is infinite, as soon as any non-zero force is applied.

Infinite acceleration results in immediate infinite velocity. It makes no sense for light to only accelerate until 300,000 km/s and then take its foot off the gas pedal.

This is why it's instead believed that there is a speed limit to causality itself.
The speed of light (as well as of gravitational waves and other massless things) just happens to be the same value, because they're going as fast as is possible.

Here's a video about the speed of causality: https://www.pbs.org/video/pbs-space-time-speed-light-not-about-light/