Questioning a DB Consultant and their recommendations
If we continue growing as a company (as we wish to), this table of
  analytics could easily hit 10,000,000 rows in a few years, and just
  keep growing.
  
  This scares me.


10M rows isn't a matter to be worried about. Even 10B rows isn't a matter for a single host. The main criteria is the throughput of the DB/engine. To prevent hangups and outages you need to be able to ingest/return the data at the rate at least 3x faster than your actual (and potential) average load. 10x is better of course. This goal can be achieved in two ways. First is the DB/queries optimization. In most cases results are more than acceptable. But every engine has its limitation that can be overcomed by some kind of scaling. Another way is the clustering, segmentation, load balancing etc. Here the DBA should pass the problem to the system architect. This is a different set of competencies. Here is the good explanation how it works:
https://github.com/donnemartin/system-design-primer