Of course the analog scopes are responsive, all the knob does is change the DC offset on the deflection grids or the gain of some amplifier or timer.
That's not *always* true. For example, the Tek 2465 Series (which is an analog scope, no digital storage) used a series of pots for the front panel controls. A reference voltage was applied to each pot and the wiper voltage scanned in sequence by a mux and ADC to determine the position. (Some of the controls even used two pots ganged together, without end stops [so they were continuous rotation]; by using two pots the direction and speed could be determined.
Anyway, on this scope the horizontal and vertical position controls were scanned, the data stored and then the deflection voltage set by a DAC. The only front panel controls not digitally set were focus, graticule illumination (though it could still be turned on an off digitally by the scope) and trace intensity.
This wasn't uncommon amongst high end analog scopes of the era. 
The Tektronix 4 channel 22xx series oscilloscopes do this as well and it is one of the things that allows automatic setup to work.
What is interesting is that Tektronix took advantage of the extra functionality that this can provide; the potentiometer controls are used as absolute encoders but when you change directions, there is a region of fine control so each individual potentiometer used as an encoder is both coarse and fine.
Considering that all of the analog inputs and outputs for the controls are multiplexed and the processor is low performance, the latency is pretty low although noticeable.
Tektronix also implemented continuous turning encoders this way by placing two normal potentiometers on the same shaft but out of phase to remove the ambiguity where the resistive elements are interrupted. These compare well to the various digital encoders and I wish they were available as standard parts. I did a search for them a couple months ago and found nothing.
Yeah, it was a very clever system and the way they transitioned from coarse to fine actually works really well.
The 2465 Series has no noticeable lag to me; everything is basically instantly responsive. This is pretty impressive as you'd think the processor (an M68K) is handling quite a lot. However, they used numerous tricks to offload tasks from the CPU. The way character generation was handled was pretty clever. The CPU simply drops the readout data onto a specific memory location and a separate circuit takes care of decoding it, reading the character data from a ROM and loading it into a DAC, byte by byte. The time multiplexing of the beam between trace and readout is also handled by a dedicated circuit.
Basically there was a data/address bus that ran across the main board and onto the expansion backplane and each module ran pretty much independently, taking a few instructions from the main processor and putting data back onto the bus. This was accomplished with nothing more than logic gates and a master clock, for the most part.
There was also a single ADC and a few DACs on the main board, which were used in place of calibration pots. The DACs were multiplexed, with sample and hold circuits to maintain the voltage when the DAC was scanning. They would also use the ADC to read back the output of the DACs, which increased effective resolution and reduced INL/DNL errors. The CPU spends most of its time reading the front panel and scanning the cal ADC/DACs.
I've looked at the M68K assembly from a system ROM of a 2465B and it seems to be very well written. They clearly had some high end programmers that knew what they were doing. The whole thing is very optimized.
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