You didn't even mention the worst part. A senior citizen can apply for a job with an income subsidy and health insurance, which is a kick in the nuts to the young people who are paying for it.
But we should definitely not tax away social security benefits for people who are already socially secure.
I'm a fan of whole-system reform. Mandatory savings in an investment account, with a benefit floor at current social security levels. Something similar to Chile. This would encourage earlier retirement, which improves employment prospects for young people. It also increases benefits for basically everyone. Rewards work of all kinds for everyone.
Social security reinforces the notion that retirement is related to age rather than means.