Yes, Merlin was designed to be cheap. That's why it's cheap. Being reusable was not an impediment to it being cheap. Being reusable is not an excuse for being expensive.
A cheap rocket engine needs a cheap development process, which means you want your test articles to last a long time. Far from being an obstacle to cheapness, reusability is a requirement for an affordable engine development program.
Let's go way back to Usenet and listen to Henry Spencer on this subject.
https://yarchive.net/space/rocket/rl10.html
"To reiterate my original point: almost any regeneratively-cooled liquid rocket engine is reusable, even if it was built for expendable vehicles. The design requirement for the F-1 was 20 starts and 2250s of firing; as part of the test program, six of them accumulated over 5000s each."
Other engines could be similarly rated for jinutes of runtime by default for maximum performance. SpaceX aldo repeatedly ststed Merlin and Raptor were designed for cheap and fregvent reuse.