I understand that there must have been a reason the current system was implemented, but in practice it is slower and more prone to error than simply allowing the user to press on a block and drag to reorder it. This would also maintain more consistency with the desktop experience, which is desirable.
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I think on top of that would be nice. If you drag multiple objects, scroll and move is simply convenient.
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Drag and drop is available on Android 
You can hold an object until an orange line appears that allows you to choose its destination location on the canvas.
See Drag and Drop Too Sensitive on Android - Feature Requests - Anytype Community for further improvement.