Well… essentially yes. It is quite a bit of work to maintain different pairs. Because of that exchanges tend to focus on some pairs and no others. Eventually as things get really popular, new pairs emerge. But even then, they are usually cross pairs unless they are very very popular.
To explain what I mean…
In forex trading today you have what are called major pairs - EUR/USD, USD/JPY etc.
For crypto that would be something like - USD/BTC, BTC/ETH etc.
So a cross pair is when you need to make more than 1 trade to get to the currency you want. This is less efficient but it brings good liquidity to the market. For example, if you wanted to get to JPY from EUR, you would actually go from EUR to USD, USD to JPY.
Till very recently, I believe that even ETH was typically traded through BTC. Meaning that if you want to go from USD to ETH, you would go USD to BTC and BTC to ETH. Now, it looks like ETH might be trading vs fiat by itself. But I could be wrong.
Anyway, long story short is that if you were to try and go from USD to PAY, it means that you need to do many changes and is something a exchange may not want to risk. Not only that, it is going to appear quite expensive to do so.
Of course, you could skip the crossing and go direct. However, you will need ample liquidity in the markets to allow that to happen, something a lot of alt coins do no have.
Long story short, it makes sense that exchanges specialize (at least for now). The same way it makes sense that there are specialized forex exchanges and stock exchanges at the same time.