The Equal Protection clause wouldn't change anything, since unemployment compensation does not violate that clause.
But, for the sake of argument, lets say it does violate it. The number of changes that would have to be made are huge. As is the number of people who would be qualified for your new & improved unemployment compensation. Unemployment compensation was never designed to provide for the huge number of people who would qualify.
And there are existing programs that provide what you want UC to take over. The only complaint you have with those programs is means testing. In other words, the only complaint you have is to show you NEED assistance to survive. You want it to cover those who can make it without assistance, but who WANT more money.