There are a few factors here. First is that the HS2 stations are already designed with higher platforms. That means that the majority of passengers will have level boarding at at least one end of their journey, a benefit that risks being lost if you start playing with the designs.
The second point is that there hasn't been some curious oversight. The original specification was built with the full knowledge that the trains would be running into existing stations. The vehicle height is lower than Pendolinos, and a step has been specified to make the process safe and completely comfortable for the vast majority of users.
The third and possibly most important point is that just because 915mm has been chosen as an arbitrary design height, the existing stations on the line don't actually have platforms at that height. Extensive work has been required to provide level boarding on East Anglia and Merseyrail. Given the range of different heights in play, it may be that the best solution is to figure out how to have differing height platforms at the stations, or to use a harrington-hump arrangement for wheelchairs.
Finally, the specification for the carriages has been designed so that they can be reasonably long and reasonably wide, can still fit within the classic loading gauges. As soon you start lowering the base you have to narrow the carriage at the bottom, which means less internal space and more need for expanding steps at the doors.
Whether it's green tunnels, floor heights or anything else, the key reason why HS2 is proving so expensive is that every single aspect of it has gone through a detailed design process, resulting in a reasonable compromise solution which is good enough for all purposes, and then at the last minute some stakeholder who is politically too important to be ignored has come along and forced a redesign so that their narrow interests take primacy. Let's just get something built