If they wanted more deposits, why would they pay as little as possible to 'keep the spread'? No bank is anywhere near monopoly; there are tons more deposits to get (if you want them, and can make money safely on a spread).
For the same reason that many businesses do not want "more customers" above anything else - to the point of selling at cost or at a loss - and if they increase prices is not necessarily because they want "less customers".
