I think it can actually work quite well, provided you can setup a separate service just for analytics. It's not too unreasonable to assume there are sites already doing this since the concept of a central repository that you alone control (and isn't provided by a third party) can be appealing.
Also, you have to worry less about privacy and just concentrate on keeping your own systems and services secure.
If there's something wrong with your DBMS where the alter table to add a row is an expensive or dangerous operation, just add a new table for every attribute, having lots of tables in a database is no worse than having lots of variables in a program.
If your DBA gets angry at you for adding new tables all the time, get a new DBA.
But, seriously, everyone rolls this themselves and does it wrong. If you've done it right, and can release it, you'd be doing good for the world.