Yes, Algebra should be mandatory. There are two core intellectual reasons for this:
1. As Matthew Levey notes, learning algebra is an essential component to developing a capacity for abstract, analytic thought, maybe even the most important one.
2. It's in and of itself interesting, even fun, when well taught. It's full of new perspectives, puzzles, and knowledge in a way that the arithmetic that precedes it for most kids is not. You can't solve algebra problems via memorization. You have to think your way through them. That may be hard for some kids, but the solution is to make curricula more flexible not to eliminate the subject altogether.
There's also enormous practical and vocational utility to algebra for a very large portion of people. People doing any sort of quantitative work use algebra (whether they recognize it as such or not). And that's not just engineers, scientists, and financial analysts. It's "knowledge workers" of almost any description, crafts people, clerical workers, small business owners, and more.
You want to be able to judge what a politician says about the budget? You're better off knowing some algebra. Judge whether the bottom line on personal financial documents like tax returns, mortgages, or credit card statements are reasonable? Figure out how much money you need to save for your retirement? Find a mistake in that spreadsheet you're working on at the office? Figure out whether A-Rod or Jeter is a more productive player? Algebra. It's woven into countless aspects of life, as important and useful as arithmetic for people who actually want to understand what they're doing beyond the most rudimentary level.
To say that people don't need to learn this is to consign them to an unacceptable and tragic level of ignorance. That doesn't necessarily mean that everyone needs two years of it, complete with high-stakes tests, but it does mean that everyone should have at least some measure of exposure to it. Plane geometry and statistics, too by the way.