Usually when I have seen the DC spike on spectrum analyzers, it has been tens of dB above the noisefloor.
Here's some fresh images from a one year old Siglent SSA3032X.
In these screengrabs the
Yellow trace is the realtime one and
Purple trace is max hold.

Here's how it looks looks when the analyzer is set for 9kHz to 100kHz span.
The DC spike is approx 43dB higher than even 14kHz.

On the 9kHz to 1MHz span we see that the spike is still shown 24dB above the noisefloor.

And even with 9kHz - 100MHz span we still see the DC spike at the start.
The only spectrum analyzers where I have not seen this has been those that don't start at low frequencies.
For example my R&S CMU200 or CRTU-RU don't have it, as their spectrum analyzer covers the 10MHz - 2700MHz span.
And while some microwave folks might call 10MHz "DC", it's still reasonably far away from 0Hz.