Yes, the probe will load the power rail in AC. But what is the source impedance of a power delivery network? Let's say it's a regular microcontroller board, with a bunch of capacitors on the power rail. Ceramic SMD capacitors have ESR in the order of tens of milliohms in the same frequency range. So the 50 Ohm loading is not that important, it doesn't really change the behavior of the circuit.
If you just AC couple, your low frequency response is not ideal. You will see the noise but you will not see brownouts for example. Also, you will temporarily overload your scope when the power rail comes online, because it will generate equally large opposite direction spikes. So more circuitry is needed. Bear in mind most power rail probes will be able to 12V or even 24V supplies, while your scope input is only rated to 5V in 50Ohm input.
Oh and scopes don't really have AC coupled 50Ohm inputs, it's almost always DC coupled. So that's why the probe.
I'm working on a power rail probe BTW, I hope to order it soon-ish.