The analog trigger rearm rate depends on the sweep reset time and not the trigger itself except insofar as it has to detect the other slope before arming. It is quite practical to have triggers which operate into the 250 MHz+ range and some oscilloscopes did this because the trigger was used for other things as well like to drive a frequency counter.
Digital triggers are just a variation of a transition midpoint timing TDC.
The LeCroy literature that I originally quoted from was for analogue triggers but in digital scopes. The trigger could be made faster by having a shorter discharge time but this would then make the time measurement less accurate.
Such an interpolation approach makes sense if the sample points are comparatively widely spaced and you're trying to catch a fast rising edge. With a 350MHz scope (1nsec rise time) and with the sampling rate at 1GS/s I can see that digital interpolation could be quite inaccurate compared to using an analogue trigger (which my scope does) but it does limit the screen update rate (my WaveJet's update rate is only a few thousand wfms/s).
I remember when LeCroy started advertising their digital triggering. They had some pretty impressive videos of them in action.
There are lots of ways to implement a TDC. Dual slope implementations have the limitation you identify and are common on low acquisition rate DSOs simply because a faster TDC would not make them any faster because their trigger rearm time is limited by how quickly they can transfer the current waveform record to the processor. It took oscilloscopes with segmented memory or DPO functionality to require faster TDCs and even then, directly digitizing the output of the TDC (time to amplitude conversion) instead of deintegrating it will get you to at least 200k waveforms per second.
http://www.ko4bb.com/~bruce/TDC.htmlSome form of TDC is needed to support equivalent time sampling. Many oscilloscopes lack this now simply because they have high enough real time sample rates but in the past equivalent time sampling was the rule.
I have wondered about aliasing with digital triggers. Jitter and nonlinearity in the digitizer will be exasperated by interleaving and the resulting aliasing from the interpolation will corrupt the trigger position but I assume the effect is small enough compared to the supported equivalent time sample rate to be ignored.
http://cp.literature.agilent.com/litweb/pdf/5989-5732EN.pdf