Some context here. That $2 wage you quoted only applies to the handful of red states without a state minimum wage amd those state's employers still need to comply with federal minimum including tips. It really comes down to the state (
https://www.dol.gov/agencies/whd/state/minimum-wage/tipped).
Definitely in those handful of red states the laws suck for tipped workers but in other states like a NY or California, people can make a much better living with tips than you'd get at a retail or low end job. It's hard to just look at a national average because it will vary so much by state. Really the min wage laws need to be reformed for those red states to not let them get away with underpaying tipped workers before tips.
The SS is an interesting point though. While I am pretty sure the difference between unreported tips being invested (even at less than 100%) will always be better long term any difference in SS benefits from reporting the increased wage, it's also true that less than 50% will be investing that extra money, at least among younger tipped workers. I'm not sure that point will convince the types of people I worked with. I'm pretty sure most would still prefer tips not be taxed.
And now there is a huge range of people included among tipped workers too, from young people working through college to less educated/skilled workers in the best earning job they can find to people working part time while they pursue other jobs/interests to retired people driving Uber for a little spare income.