I was thinking more that they would have to schedule around anything that CBS already shows (if they do - I don't remember specifically which station shows which ones, but there are usually at least NYC, Boston and Washington DC events televised) and probably more important that many people would be attending local events that evening meaning that they wouldn't be home to watch anything on TV, which would lower the ratings even more than a normal Saturday night (since oftentimes the 4th events are things that a whole family goes to).
That doesn't mean they couldn't choose to offer one, just that they might think twice about doing so, if they are trying to get people to watch it that normally don't watch the daytime version (as kind of an ad to encourage more daytime watchers).