While pardon power originated from British law, the reason we kept it was what the OP referred to (see the federalist papers [1]).
When forming the government the founders didn't just blindly copy British government. There was a lot of debate over what to keep and what to omit (For example, we don't have a king. Presidents were seen as servants not as rulers).
Pardon power is mostly a direct copy of British pardon power. However, there was a reason for that beyond not getting around to reform.
It should also be noted that presidential pardon power, while very powerful, isn't unlimited. The president can only pardon federal crimes, they cannot pardon state crimes. That's an important break from British law where royalty had(?) unlimited power to pardon any crime. Particularly when pardon power was first envisioned, the founders looked towards a very small federal government. In that case, the number of federal crimes were far fewer than what we have today. That means, the presidents pardon power was pretty much only for crimes such as treason.
In other words, absolutely the founders were influenced by British government. They weren't, however, just blindly copying things. Everything went through debate.
[1] https://avalon.law.yale.edu/18th_century/fed74.asp