^^some tankless units have a small “buffer” tank, but i would guess the main reason you have the slug of cold water at first is because the water in the piping has cooled down. have you tried insulating the piping? a return will allow for more consistent temps but only if other fixtures are being used to allow circulation. low flow fixtures can cause longer times to get hot water…takes a long time to empty piping especially considering its over sized for those low flow fixtures since most codes have yet to be updated.
with how quickly tankless heaters can heat up it doesn’t make much sense to still retain a tank. heating water in a tank all day when no one is home to use it? yeah…makes sense.
my house currently has a NG tank type water heater. i hate it. especially when the dishes are being done when i’m in the shower. and we don’t even have a dishwasher. running the clothes washer is a guaranteed cold shower. i will definitely be going tankless.
The pipes are wrapped well and when I had a tank, I didn’t have this “issue” I put issue in quotes as it is a SMALL trade off for NEVER having to worry about running out of hot water again! I remember when I first installed it my GF could not wrap her head around the idea that the only way we will run out of hot water is if the lake dries up while we are showering or if the natural gas is depleted in the earth.