Why would the loss of water be any worse than with any other water heater? The length of the pipe run from the water heater to the fixture is the same regardless of the water heater type. And a tankless produces hot water in a few seconds (10-15 on our spec sheet).
A couple of reasons. 1) tankless water heaters have a minimum flow (usually around 2gpm). Until that flow is reached, they pass cold water. 2) a water heater starts providing warm water to the pipe as soon as the faucet is opened, plus even with anti-convection inlets and outlets, water heater tanks do heat the pipes and water adjacent to them, giving a head start, 3) US installations tend to have one tankless feeding a whole house, which means larger diameter pipes, and more cold water dead volumes.
Per your specification sheet, even at a low flow faucet in California, at least 0.3 to 0.4 gallons have to pass through before the heater before it turns on, plus of course all the water in the pipe between your point of use and the heater. (And I agree with you that the piping volumes are similar.)
For folks who have plumbed, or replumbed, in PEX, PEX piping has a lower dead volume for a given flow rate/pressure drop, and it is often plumbed out of a manifold near the point of use, further reducing piping dead volumes. So, a tankless heater with PEX will do better than a tankless heater with copper, or galvanized, or PVC.
My big picture: tankless heaters do have advantages as they don't waste energy keeping water hot. As a personal opinion, I think that tankless do best when they are situated at the point of use, so you have only inches of pipe to fill with warmed water. While that type of installation is common in other countries, it isn't the typical installation practice in the US, where the tendency is plumb up only a single tankless for a whole house, and that tends to leave large dead volumes of water in the pipes that is wasted to drain (usually) waiting for the hot water to arrive. So, I think that there are trade offs. The clear winner in energy and water efficiency is probably a heat pump water heater with a recirculating pump that uses less over all energy and enables instant point of use hot water. Not currently very common...
All the best,
BG