Generally 50

inputs on scopes don't have a DC blocking capacitor and are DC coupled, which usually limits the maximum DC input voltage to around 5V to avoid excessive power dissipation in the 50

termination resistor. If you did have a DC blocking capacitor in the scope you would need a really large one (some 10's of uF) to get any sort of useful low frequency (<1kHz) response . Such large capacitors have a lot of undesirable parasitic elements eg. inductance that are not conducive to accurate measurements at higher frequencies where the 50

input termination is normally used.
Measuring PSU noise with a scope using a quality 10M

probe would be usually sufficient unless you are interested in measuring noise components >100MHz where the 50

termination will give better signal fidelity and more accurate measurements. With a 10M

probe selecting AC coupling on the scope input has much less effect on the low frequency response and you can still get good measurements down to low frequencies (<10Hz). However, obtaining good signal fidelity and accurate noise measurements with a 10M

probe requires careful attention to the grounding of the probe: use the shortest possible ground lead on the probe and connect it as close as possible to the circuit point where the signal is being measured.
The situation with spectrum analysers is different; these almost always have a fixed 50

input with no internal blocking capacitor. The input to a spectrum analyzer can't tolerate any DC voltages as even a small DC voltage (<1V) can destroy the input mixer diodes. This is why the connection diagram shows the blocking capacitor as this is essential for the spectrum analyser. You could go even further and add a power limiter to spec analyser input to protect against the voltage spike that occurs when the DC blocking capacitor charges up. Such a power limiter would be recommended if the PSU under test has an output >10V. Otherwise set the input attenuation on the spec analyser to its maximum level to protect the mixer diodes.