What happened to all of the Dynamic Signal Analyzers?
Ah yes, the HP3561 100kHz DSA, I remember it well. The first 'difficult' problem we used it on was the stabilisation of a thermal servo loop. With a characteristic times of minutes, those mHz were needed.

The key to its time-limited usefulness is that that was back in the 1980s, when my thermal control loop was analogue, and ADC/MCU/DSP/DAC systems were uber expensive or non existant, certainly unheard of for low cost servo work.

Now, 99% of servo designers would start with an ADC/MCU/DAC system, simulate the system with LTSpice or MATLAB before they built real hardware, and be able to capture live data from the system and analyse it. The test gear is built into the system, or is only a LAN port away!

That's a view from the application side. Looking the technology behind the front panel ... what those instruments were doing was building on some serious state of the art hardware. The HP3561 used the first 250ks/s ADCs with decent dynamic performance, long before they were readily available on the open market, with TI 30xx DSPs offering 10M ops/s behind them for signal processing, this was bleeding edge in those days.

Instruments that do that still exist today. The ADCs and DSPs have moved up to Gs/s, so they are aimed at different applications/markets, and called something different.