Did you mean you put a recirc pump on a tankless heater? How would that even work?
I can tell you I have saved plenty of money with mine during its 12 years and counting of trouble-free, maintenance-free operation. I suppose they're not for everyone, but they work well for us.
Hot water on demand in larger houses are a big issue when the unit is mounted in the basement and the there a bathroom on the third floor, we always install recirc lines in the houses, the times we havent we have 100% of the time got complaints that it takes forever to get hot water to the furthest fixtures, we are on water meters here and paying to run cold water for 60 seconds to get hot water is a big deal for most people.
Without a hot water tank or at least a holding tank the water cant radiate heat down the line, hot water on demand leaves the water lines cold ecspecially with the new houses that all use pex, insulating all the water lines is one way to combat it but thats nearly impossible in an old house. So recirc pumps keeps hot water in the lines all the time, but theres a efficeincy loss associated with it as well, all the mechanical companies here were installing hot water on demand for years but in the last 5 years i bet 95% of new construction has gone back to the standard hot water tanks due to waranty issues and customer complaints and break downs with the tankless water heater.
Heres on scenario: customer calls: no hot water, worst case scenario with a water tank maybe a $100 gas valve or a $10 thermocouple that any wholesaler carries in stock, youll have hot water in a couple hours
Scenario 2: a navian or rannia instant hot water on demand goes down, probly 2 hours to trouble shoot the thing, try flushing heat exchanger, may e needs a gas valve, gas valve probly in the ball park of $500 give or take, nobody has any in stock because there one of a kind unit specific, so ill order one, hopefully be here in 2 days, air frieght right from navian or rannia, $1000 later and 3 days without hot water you should be good to go until the flow switch seizes up, now we have to tear it down again.
Ive delt with these things for years, maybe im bias because i only get the service calls for broken ones, nobody calls me to tell me they love there unit. But i do know i get way more service calls for instant hot water over conventional water tanks and the repair bills are 5 times what a conventional water tank repair would be.
In my experience, and i have a fair bit, ive been working for mechanical hvac companies for 20 years, i can easily name 5 good reasons not to buy a hot water on demand system, only reason i can think of to buy one would be space, not enough space for a water tank.