My impression is that quartz crystals as found in oscillators are so brittle that it's hard to use them for things like this; I guess PZT (lead zirconium titanate) is more robust somehow? There are also polymer-based piezo materials, like PVDF.
That being said, there's a type of radar system called "stepped frequency continuous wave" radar that uses a bunch of single frequency transmissions instead of an impulse transmission. The basic idea is that instead of using a high-bandwidth transceiver to send and receive the impulse, you can use a low-bandwidth transceiver to send and receive tones, and then hop this transceiver over the large bandwidth to get a high-resolution image (the tradeoff being that it takes longer to acquire an image). Since ultrasound is basically radar, I'd imagine this technique could be used for ultrasound too.
Typical radar works by sending and receiving a high-bandwidth impulse, which requires high-bandwidth transceivers. Let's say that transmission occupies frequencies between f0 and f1. SFCW radar works by sending a bunch of individual low-bandwidth transmissions between f0 and f1. So each transmission is small, but together they occupy the same f0 to f1 bandwidth. Assuming the environment didn't change in the time it took to send all of those low-bandwidth transmissions, you've effectively simulated a high-bandwidth impulse using a bunch of low-bandwidth impulses. So the spatial resolution will be the same.
And if it can't withstand the vibrations it generates, how far off would it be from the required energy (many orders of magnitude?)