As for multi-coin payment processors...the number of coins they accept will be limited by liquidity and almost no other cryptos have sufficient liquidity to support significant commerce.
You must have edited this in, or I missed it.
Popular coins probably can handle it. That gocoin thingy that supports ltc and gift card purchases, for instance, also accept dogecoin. And I believe they have nxt planned soon too.
So you are right in the sense that no, not every alt will be accepted. But it will be more than just ltc. It already is.