There are already competitors operating here in Canada doing this stuff fortunately. I believe Amazon acquired one of them which turned into this [nm, see edit]. That should hopefully pressure Amazon to expand and this will offer tons of free advertising for those smaller companies competing.
Edit: turns out it was Buffer Box and they were acquired by Google and (of course) shut down https://www.wikiwand.com/en/BufferBox
InPost is another one with boxes all over Europe. They recently shut down in my city though :/ (Toronto). But otherwise it looks pretty like they have extensive deployment: https://inpost24.com/
Germany has DHL Packstation: https://www.wikiwand.com/en/Packstation
Also two startups: https://wefunder.com/swapbox and http://www.ucella.com/