That exponential dependence comes from the use of chemical rockets, which have a pretty firm upper limit on their exhaust velocity. Once in space, lower thrust could be used, which admits the possibility of higher exhaust velocity. If one can vary the exhaust velocity then the problem can be evaded (although the specific power (power/mass) of the vehicle must be allowed to become very large, or else acceleration will decrease.)

Recent example: https://phys.org/news/2022-02-laser-mars.html

Note the very high specific power. High Isp rocketry is all about the heat dissipation.