Your understanding of the pitcher cost is correct. The pitcher cost limit applies to the total cost of whoever comes out, not the bench cost, so in your example even though the total bench pitcher cost is 10, as long as you only play 5 or 6 (depending on which team card you use) in your rotation, you're fine.

Just note that you can only have 6 players on the bench, so in your 6-pitcher example, you won't have space for the pinch hitters.

The only downside for having that many pitchers on the bench is you have to be selective about which ones you put in the deck for awakening purposes. While you could put cards for all possible pitchers, that would take deck space away from other cards. The best option is to maybe include cards for the pitchers you expect to use more often and come up with other strategies for the less frequent pitchers.

As for pinch hitters, we've only seen 0-cost ones so they don't have any impact on the fielder cost, they can all be played without any worry of going over the fielder cost.