1. Amending the law is relatively simple: replace any instance of only one with any when it comes to election laws regarding marking the ballot.
2. Amending the ballot is a minor change: just allow anyone to mark any (including none or all) of the bubbles representing each candidate on the ballot. The language on the ballot itself barely changes, the structure of the ballot can and would be identical to today's ballots.
3. Explaining the method to the public is dead simple: there's a pattern here, "instead of marking just one, now you can mark any of them" is a sentence that anyone can understand and implement. Explaining the calculation ("whoever gets the most votes, wins") is also dead simple.
4. Extending to multi-seat races is trivial: just take the top n vote-getters instead of the top 1.
5. It appeals to intuition: it does feel like "cast one lot per candidate you approve of" and aggregating that across a population is a fair way of distributing consensus. "Approval" means many things to many people but it is still a clear subjective threshold for each person. This also means that voters will consider the result harder to dispute on the grounds that it doesn't represent the people's will.
6. Tactical voting is straightforward and hard to do wrong: for what it's worth, tactical voting is always an option, and people are always going to use it. It's just how things work, at least for the foreseeable future. That being said, of all the systems, approval voting makes it the simplest to engage with and the least underhanded. Vote for people you want to promote in the election, don't vote for people you want to suppress in the election.
I really don't see the downsides. Deep in the discussion boards of the internet where the election nerds lurk, they complain about this or that theoretical imperfection. But as for the options that have been suggested, this one stands out as the easiest to adopt societally, with the most bullet- and fool-proof implementation.