Why is Computer Architecture in $2^n$ bits?
Not necessarily, for instance, look at the memory bus width in modern day GPUs, they would have values of 192, 384, 768(while 128, 256.... are common).

One could argue that 192 is a sum of powers of 2 (2^7+2^6), sure, but what number isn't?

That being said, any memory modules directly associated with a microprocessor or a microcontroller will have capacities in powers of 2. Traditionally registers will be 8,16, 32 or 64 bits long (though 10-bit and other non conventional widths exist).

A processor (or controller) with an n-bit register can address upto 2^n addresses (i.e, 0-(2^n)-1 bytes). Hence without changing the processor, one can extend the memory associated with it although exceeding the addressing space beyond what the processor can manage will be redundant.

In many DSPs, the memory associated with the processor is in 2^n multiples as many of the signal processing algorithms can be made very efficient when calculating this way.