There is still a limit you would place on acceleration for comfort purposes.
In my modelling I've used 1.3m/s/s which is what a tube train accelerates at. A high speed train with 5-7% battery mass will have about 3x the power of a conventional EMU and will manage to accelerate at that rate past 100mph.
This basically means that you can get up to 125mph in about 1500m. Comfort standards in the case of acceleration and braking are for the guidance of the wise and the adherence of an industry that wants to be destroyed. Buses aren't limited to the same degree, passengers still stand on them and move around even though buses accelerate and brake at up to 2.5m/s/s in normal operation and 4m/s/s in a hard stop.
In practice passengers will adapt to higher accelerations especially if they result in faster trains, cupholders and similar are relatively cheap.
Internal combustion engine cars are limited by a narrow torque range, while electric cars aren’t. But the tyres and weight still matter. Diesel-electric trains have the same wide torque range as electric cars, I believe. Diesel alone cannot accelerate like diesel-electric or electric (or diesel-hydraulic?), but that isn’t the comparison being made.
Battery life concerns may remain while the new generation of batteries try to show this is outdated.
EMUs are ultimately limited by the OHL infrastructure, battery EMUs are limited by the discharge rate of the battery. Once you get up to 5% of the trains mass being in the battery the discharge rate that the battery can manage is massively higher than what we would expect from an EMU of that size.
The second big advancement due to BEVs is that traction motors are now commodities, any of the larger car markers now builds more traction motors in a few months than the entire rail sector has ever used and these things have very much higher power density than anything being used on rail. This means that tripling the power output of the next generation of BEMUs will be pretty trivial from a cost/mass perspective.
What is wrong about the current experience and assumptions around how fast a modern electric train can accelerate? The 80X's don't hang around on electric power.
Try driving a decent BEV, see above points on the quality and cost of the parts/engineering. Rail is going to be buffeted by the electrification of road transport, self driving, AI and electric flight, we need to think bigger or become irrelevant. A BEMU service with rapid acceleration could allow us to turn much of the UKs rail network into high speed metros, no need to run mixed traffic.