First spike latency or similar measures when looking at ensembles only tells you about the latency of the least affected unit when you are talking about latency increases, or the most affected unit when you are talking about decreases.
For example, if you record from 30 cells on a multiunit cluster and the latencies of 29 of them increase but 1 does not change, you might conclude no effect on latency.
Also, changes in detection probability can be harder to recognize in multiunit recordings. If a pharmacological manipulation increases or reduces activity overall, including at distant sites, this might change your threshold of which cells' spikes you can accurately detect as spikes by increasing or decreasing the noise floor.
For example, if your threshold decreases, you might be recording spikes from ~20 cells in your control condition, but then sample from ~50 in your pharmacological manipulation. Note that in this circumstance the total number of spikes you record might actually go down, but you would underestimate the affect because you don't know how many cells you are actually sampling from.
Of course there are problems with single cell recordings too. Sometimes it's really the ensemble activity that matters more, in that case the single units aren't as informative. You also have the problem of tracking accurately a single unit throughout a pharmacological intervention, which can be problematic depending on the time course of the manipulation (electrodes drift, cells die) or if the manipulation itself affects spiking properties (it may be more difficult to ensure you have the same cell if spike widths or amplitudes change).