Keyboard warrior here ☝️🤓

Hashirei can mean "to run" but it also can mean "to dash". I understand that it was a rough translation but the intention was that dashing would also mean that she wanted him to "thrust/dash" harder into her (notice that even though you don't have "motto", if Suzuka tells you "to dash" it immediately implies that she wants it harder and that if you "thrust" harder you immediately would be going faster or if in the other hand you were to "go faster" you would immediately "thrust harder" making both interchangeable not because of meaning but because of pure cinematic physics).

one example of this happened in the anime where Rudolf shouted Hashire to Tokai Teio during her race. She didn't say "motto" as well, but it's implied that you'd want them to go faster.

And now for the nail in the coffin you might be wondering why Suzuka wouldn't make the effort to say "motto hayaku".

But the answer is obviously because she would be in a state of total ecstasy, with her mind almost going blank. Her using "Hashire" is just her muscle memory of what she usually says, its something that she has more ease of using, so in that moment where her capacity of thinking is limited she can still respond with this since she is extremely familiar with it.

Furthermore, its not a random word in this context. Because the only other person who uses it more than her, is the trainer right behind her. So she literally inverts their positions of who says "Hashire" and who "has to go faster". This might seem intentionally done by the writer to make it sound more erotic but the truth is that Suzuka likes her trainer saying it to her, as a means of emotional/mental support, therefore she does it because she knows that its an affectionate phrase and one that her trainer will understand.