Why do the re-engined narrowbodies get new type designations?
 

You need to define what you mean by performance. If it's as simple a $$ per seat mile, it has no relationship to Cert basis.

If it's altitude and/or stall characteristics than likely a designator etc.

Type designators are used for planning by airports and fire services (ARFF), as well as ATC.

I'd guess any notable changes in characteristics or dimensions such as weights, door heights, engine ground clearance (e.g. neo and Max), sharklet-heights, fueling points, internal aisle widths, etc. are going to be worth flagging for those ground planners.

Even if they are unimportant in 99.9% of ground operations, there may always be one gate somewhere where the little differences could result in a ripped sharklet or a dented nacelle, unless designated.

All true, although many of those distinctions (sharklets, internal config, etc) are catered for by different IATA codes while still using the same ICAO designator.

These differences mentioned is important for maintenance providers too, at least if company is having more than one customer to take care. Some operators let you in to their own systems, some not -> need to rely airport information system for times/types etc etc.
We have currently customer flying randomly A32x CEO and NEO. This need to be known before arrival just in case we need to do something, not all guys trained/approved CEO vs NEO. Same with 737 CL/NG.