The message rate does correlate to the number of aircraft, however it’s not a linear relationship due to the practicalities of the ADS-B protocol and how it’s used in different regions. It’s a non-cooperative system, where each aircraft transmits without consideration for any other transmission taking place on the frequency. This isn’t problem usually because the transmissions are very short.
For few aircraft, this means the relationship is somewhat linear - more aircraft means more messages. What happens when it is busier however, is that these messages start to overlap with each other. This can mean that some get garbled or lost completely, but since there are many transmitted the information does usually get through. ATC call this FRUIT (false replies from unsynchronised interrogator transmissions), and refers to the fact that many messages are transmitted in response to a request from an ATC radar site. If there are many planes visible from many radars, as is the case in Europe, it results in a lot of transmissions which inevitably talk over each other.
In addition, 1090MHz carries a lot of other protocols as well as ADS-B. Mode S, which is a response to a radar request that gives all sorts of data - Mode A/C which is the older system giving altitude and transponder code. ACAS/TCAS which is the collision avoidance system where aircraft talk to each other all use the same frequency. Some of those systems also regulate their own transmission rate when it is busy.
The effect is that as the number of aircraft increases, the number of messages received per aircraft reduces even though the overall message rate might still increase. You can see it here:
At night, the number of messages per aircraft is a lot higher than during the day when it’s busy.
Some regions such as the USA don’t interrogate aircraft quite so aggressively, so they might have a lower message rate for the same number of aircraft compared to a receiver in Europe.
This graph shows the correlation of messages and aircraft:
It also shows the difference between an rtlsdr receiver (most of the blue dots) and the airspy mini, which has better dynamic range and sample rate, so is able to distinguish overlapping signals much better.