Tag Admin encounter slowness due to the large number of tags that are referenced by content. This slowness is also seen in the Tag Input widget.
The is caused due to the loading of the entire tag tree at the beginning to provide client-side auto-completion and check for existence/categorization. If there are many tags loading the tag tree json via ajax, it can be very slow.
This issue is fixed by CQ5.3 FeaturePack package #29484. Please raise a DayCare ticket to obtain this package.