No wonder you save money on your gas bill, by the time the water gets warm in the kitchen you’re already done cleaning it.
The difference in time that it takes for a tankless heater to send you water should be no different than a tank unit , assuming they are located in the same spot of the water flow. I have two zone tankless heaters , both located at zones of usage. The bathroom/kitchen take no ore than about 30 seconds to deliver 135 degree (F) hot water at a 6gpm (this is a rinnai ubit). If youre having a "time of delivery" problem, Im proposing that theyve mount3ed it too far from your water use area. Its kind of dumb to even have the plumbers so locate a unit, especially since the whole benefit of these things is proximity to where you need it. If it isnt improperly located, it sounds like yopuve got a 3gpm delivery unit. DO you have a 5 gpm faucet and line? That could be your problem too.
Plumbers need watching too.
I have 2 Rinnais and we love em. I can shower all day, my wife can have a load of wash and qwe can be doing dishes without the booster heater on the dishwasher even kicking in(The kitchen upstairs bath have a 6gpm unit set at 150 degrees F).
Your savings may be based upon a fact that youve only got 1 pwerson on the line. Weve had up to 5 people doing separate things and have always run out of hot water in the past. Whenever the kids come home and we are all in competing uses, we never have a decrease in hot water and our savings have been substantial especially with the "summer/winter" hookup of the old oil burner requiring it to come on and just heat a tank full of water every 30 minutes ALL DAY AND NIGHT.
Now we have a propane system for heat and a tankless system and weve saved total pf about 120 a month the last two years(Normatized to a BTU/BTU basis not just fuel cost. If I just figured the rising fuel cost my savings would be more (And the weather these last two wintrers has been brutal).
MY thoughts about yours are
1location of the unit v the lengthy the hot water travels compared to your ould "non tankless system"
2water delivery v heater capacity. I know the 6 gpm sytems cost about 3000 with an in line temp sensor.