Edit: there is a hack where it can work, but it requires convenient piping layout and limited flow.
The general problem with tankless is the faster the flow, the more electricity you need. You need a LOT of electricity. There is no halfway - if you do not have enough electricity, then you generally get tepid water. On some, flow continues anyway, and you get tepid water. This is a very miserable experience. On others, the heater restricts flow, but you're still mixing in cold water, so the mix goes tepid also. Thermostatic mixing valves can't add more hot if it just isn't there.
Heating water takes a tremendous amount of energy. My rule of thumb is 10 kW (40 amps) per GPM to lift 40-50F outside water (hold that thought) to comfortable temp. A "California" shower head is 1.5 GPM and a regular one is 2.5 GPM, so we're talking 60-100 amps of power.
The British have a thing called an "electric shower". These are 8500, 9500 or 10,500 watts and sit right at the showerhead (often in the shower stall!) and are tankless real-time water heaters. On some of them too, the electric shower IS able to curtail flow so they don't go tepid, they reduce stream.
All that to say, your plan doesn't work because it only has two possible states, "fail" or "redundant and wasteful".
- If the tankless is too small for the flow, the shower is unusable and you must wait for hot water anyway.
- If tankless heater is large enough for the flow, you don't need the tanked heater AT ALL. So why is it even connected to the tanked heater? That only results in a long pipe full of hot water being abandoned every shower. Just plumb the tankless off the local cold water line and done.
The hack, though
There is only one "hack" that I can see working here. The pipe from your water heater to the shower - is it inside the building's insulation envelope? Often done in the snowbelt to avoid pipe freeze. If it is, then the resting water in that pipe is at 70°F not 45°F, and you'll need somewhat less tankless heat to get it to usable temperature e.g. 105F in a shower. You are going 70-105F (+35F) instead of 45-105F (+70F) so you need half the heat or 5 kW per GPM. That combined with flow restrictions could get you within reach of an achievable tankless.
And if you can make that hack work, you still don't need the tanked heater connection. The logic of the tanked heater is that after the 70F water resting in the pipes is used up, you must take from the tanked heater otherwise you'll be taking 45F cold water from the street. No, you don't need to do that! You can use a Waste Water Heat Recovery System which is a fancy name for two concentric pipes. The drain water goes through the straight inner pipe (for ease of snaking) and transfers its heat to the water in the outer pipe, which feeds the tankless heater, raising its inlet temperature well above room temp. So again there is no need to feed a tankless from a tanked heater.
