I understand that people with a data cap of a few GB and no Wi-Fi could end up being unable to download the tokens before the end of the month. For example a friend of mine stopped showing up in video calls with a group of friends because she's saving her GBs for the video calls she has to do for work. She should be spending a few Euros more per month but it's easy to wish with the money of other people.
DP3T is exploring various options for this, smallest daily proposal currently being 5MB, bigger picture download around 100MB. Worst case mobile providers could always be compelled to exempt this from data usage. That aspect seems pretty solved.