Eh, it depends on what you're calling "the signal of interest."
A spike train, the output of a neuron, can reasonably be represented as a binary signal (1=spike, 0=no spike) at 1 kHz. In fact, I'd say this is nearly standard.
The neuron's membrane potential, a combination of its current inputs, intrinsic properties, and recent history, changes on faster timescales. Whatever processing the brain does probably does not use this information itself, but one probably wants access to it anyway for experimental and practical reasons.
The signal that an extracellular electrode picks up isn't that 1 kHz spike train. It's many of them mixed together and you'll need finer features to tell them apart. In other words, you can't just invoke Nyquist, sample at 2 kHz, and call it a day.
I've written multi-tetrode cluster analysis SW. It is very much not simple. Deconvolving all the inputs is terribly difficult and computationally expensive. Generally we had undergrads as classifiers for the clustering ML, which never really worked all that well, TBH. The higher the sampling frequency, the better the spatiotemporal resolution, but the more data to work through. When you do get a cluster, the overlaps are very close together and it really is hard to say that they are 2 neurons. It takes a lot of data/time to be certain.
One thing to remember is that noise is a huge problem with all this. Not just the 'normal' electronic sources (how do you ground a brain well? It's intentionally evolved to be nothing but loops!), but the neuronal too. Neurons will often fire just because (or not), they will jiggle with animal movement, they will move with heartbeat, and they will die off or move on their own, the electrode dances about, the brain attacks the electrodes, some portion of the electrode snaps off, etc. It is a very hard thing to manage well.
(By "modern" I assume you mean densely-spaced [~10um] multi-pad linear silicon probes, the NeuroPixel being the most celebrated example among the non-specialist public.)
What many pads close together can give you is the potential for the waveform from a spike nearby to register on more than one pad.
In theory this should make spike-sorting easier, because you can distinguish two neurons whose spikes might have the same waveform on pad #1 but different waveforms on pad #2.
In practice, spike sorting improves, but not by as much as you'd think.
Part of this is down to physical factors (which are improving): probe geometry, pad shape, pad material, pad impedance, and so on.
Another part is down to software (which is also improving). Single-channel spike-sorting is by now probably close to as good as it's going to get given the information content of its input, and the algorithms and software to perform it are well-understood and stable.
Algorithmic approaches to multi-channel spike sorting, however, are the subject of active research with multiple promising avenues of progress, and software to perform it is ... well, charitably, let's call it "rough-and-ready." (It's nearly all lab-grown software, which means it's written by enthusiastic amateur programmers [among whom I'd count myself, no shade intended here] who soon move on to new projects because of the structure of academic science. This means the software is buggy, poorly documented, inconsistently supported, and constantly evolving.)
Now, using dense silicon arrays does markedly increase the rate at which I can record well-isolated neurons, but a significant part of this increase is just having more pads in the target brain region - many of the neurons I get from these multi-channel spike-sorting programs only show significant power on one or two pads.
And all of this doesn't even touch on some of the significant challenges that come with using multi-electrode arrays, including higher initial inflammation, later gliosis, and data-collection and storage (a 64-channel array [NB: the NeuroPixel 1 can record from 384 pads] producing 16-bit ints at 20kHz [just about the minimum sampling rate for decent spike-sorting] generates a bit less than 10GB/hour - a volume that real big data people might laugh at, but it sure isn't small!).
And finally, all of this is done off-line. On-line spike-sorting is harder.
So I'm sorry to say that just having a modern multi-electrode array absolutely does not make things "quite a lot simpler."
A spike train, the output of a neuron, can reasonably be represented as a binary signal (1=spike, 0=no spike) at 1 kHz. In fact, I'd say this is nearly standard.
The neuron's membrane potential, a combination of its current inputs, intrinsic properties, and recent history, changes on faster timescales. Whatever processing the brain does probably does not use this information itself, but one probably wants access to it anyway for experimental and practical reasons.
The signal that an extracellular electrode picks up isn't that 1 kHz spike train. It's many of them mixed together and you'll need finer features to tell them apart. In other words, you can't just invoke Nyquist, sample at 2 kHz, and call it a day.