Why does medical ultrasound use pulses instead of chirps?
There seems to be a fairly large number of papers on the subject of pulse compression in medical ultrasound according to Google.
The main reason to use pulse compression (ie using chirps) is to increase the average transmitted power to increase SNR but it does come with its own set of limitations, such as increasing the minimum range response and ambiguities in the presence of doppler.
It is used with radar because the available amplifiers that can provide high-quality output are limited in power (especially with semiconductor PA) but even TWTs can't provide the peak power that magnetrons do. Magnetrons however can't provide the signal quality needed for sophisticated beam-forming and don't integrate well with modern electronics.
If the transducers can provide adequate SNR without using compression, there is not much reason to use it.