My primary reason (16 years ago) was tub-filling, followed by space savings, followed by longevity & low catastrophic leak potential compared to tanks. With standing pilot ignition and a 78-80% raw combustion efficiency it was no super-saver but it probably paid for itself in fuel savings in that time frame (and if history at this house was any guide, I would have been replacing a tank before now anyway.)
I only retired the tankless when I retired the 5x oversized cast-iron boiler, to be replaced by a Takagi KD20 tankless, used as a wall hung boiler, serving a reverse-indirect to buffer newly implemented micro-zoning and provide DHW.
Were I totally kermit-complected I might have run a mod-con instead, but the calculated fuel savings of the higher efficiency didn't go NPV+ within the anticipated lifetime of the mod-con. (Lessee, a $400 surplus tankless, or a ~$2800 mod-con, that's a $2400 cost delta... at $80-150/year annual fuel savings, assuming 3% discount rate... nope, still negative at 20 years)
And the tankless gives me WAY more first-hour gallons than an appropriately sized mod-con would. Without running it even as high as 1/2-modulation, with a drainwater heat exchanger feeding the indirect I get "endless hot water" at a ~4gpm gusher in showering mode, and can still comfortably fill the tub using the thermal mass of the indirect, maintained at a modest 130F (heating temp required by the radiation on design day, so WTF, use that temp for the DWH and forget about it). Even when pulling heat out of it at ~1.5-2x the design day with an air handler coil (the 2nd stage of a 2-stage zone) showers run forever with the tankless, but might eventually become tepid with a tiny mod-con.
So, with a tankless running as a boiler I can waste all the hot water I want- SUCCESS!!
And if the miserable Takagi beast craps out in only 5-10 years I can replace it with another $500 tankless (maybe even a cheap condensing version will be available by then) and still be $ ahead. If the price of fuel quadruples in the short term I can revisit the present-value of a mod-con against future savings, but the indirect/buffer and will stay integrated with the heating system (return water from radiation at the bottom of the tank is well in to condensing temps under a real heat load, as well as when under heavy DHW load. It'd average over 90% combustion efficiency, if not over 95% but would suffer very low cycling losses.)
But the last thing I'll be buying is another standalone tank, eh? ;-) (Not that there's anything WRONG with that...)