Truckdiag - The system you show is very complex and covers both DWH and radiant in a combined system and pretty clearly uses a boiler. Thus the need for the heat exchanger for that whole set of radiant loops.
The exchanger is there because you do not want the gycol going through a tankless boiler or any boiler for that matter. Once again your system working proves that it will work without. You have stated that hard water is the route to all evil in a tankless boiler system. We are saying gycol coming in direct contact with the heat exchanger in the tankless boiler may very well play a bigger roll in tankless boiler failures. He(son) seems to think that the direct contact is causing the gycol to break down. That has been my sons experience and he has replaced a lot and re-piped and installed the exchangers. The buffer tank he did not want to explain or maybe couldn't all I got was a 40 gal electric hot water heater is cheap, why not use it.... I'm not convinced you need it with a tankless boiler and I will not be using one in the barn addition.
"Typical Radiant Heat Floor System Operating Temperatures. Typical radiant floor systems operate at 85 - 125 ーF water temperature entering the tubing, and put the floor surface temperature about 5 degrees above the room thermostat set temperature."
We googled it your water temps seem high especially for your home. I can see higher temps for a shop where you get times of high heat lose. 120 still seems high. My son and I discussed this at length also, a system could be designed for those temps. IMO at those temps it will cause a feeling of on and off or warm and cold in the home and therefore not get the true benefit of what radiate heat has to offer. 80-90 degree water circulating through a concrete slab should keep a home toasty warm, such that you never know it is there. Giving you the true benefit of radiant heat. With radiant heat you can actually set the thermostat lower than with forced air.