That would be a rather unusual move. The 2.5 MHz Z80 is well within Mostek's (*1) base technology of 1976 (*2). In fact, already the the very first mask set of 1976 yielded 20% good for 4 MHz (*3). So they they started with 2.5 MHz, higher than anything from Intel (*4) and introduced the 4 MHz Z80A as standard part in 1977. At the time the 2.5 MHz version became the marked-down (and soon discontinued) version (*5).
It's the RAM that wasn't up to speed. Tandy was a very early adaptor of DRAM - which at that time were not exactly fast. The basic Model I had 4 KiB using Mostek MK4096 RAMs. Of which only the fastest grade (-6) would be good for a 2.5 MHz clock, while 1.77 is about what a -11 needs to stay barely in spec. It would have been a strange move to design a low end priced computer for the most expensive RAM grade.
The expansion unit (and the later 16KiB model) used MK4116, which could go faster (~3 MHz), but at that point in time the basic speed was already set.
There were in fact a lot of modifications available to speed the machine up, except most wouldn't work with the 4KiB version. The most simple was changing the 74LS92, used in divide by 6 mode, or a 74LS90 in divide by 5 mode, resulting in 2.13 MHz operation. This worked on most Model I - in fact, Tandy did it as well for the Model III. Anything faster than that (and sometimes even that) resulted in an unstable machine unless wait states were added for memory access, effectively slowing it down by 50% again - so it needed the CPU to run at least at ~2.5 MHz to make it a bit faster than the basic 1.77. That's why next to all commercially available speedup included a wait state generator.
Of course the notoriously bad clock handling in the expansion unit made any speedup a gamble.
*1 - Mostek, not Zilog, produced the first Z80 processors. Zilog was a fabless company (p.3 and p.7 of Z80 oral history). It wasn't until a year later that they had a fab of their own, using their now parent company Exxon's money (p.19). From that point on Mostek was their first second source.
*2 - Mostek, like Synertek already used a depleted NMOS process allowing much higher speeds, which Intel shunned at the time - another reason why Faggin et.al. left Intel in the first place; they wanted to go ahead.
*3 - See p.12 of the Computer Museum's write up of the Z80 oral history.
*4 - At that time Intel offered the 8080 as 1.5 MHz and 2 MHz.
*5 - Not many non-letter Z80 found in collections :))