Sure Lat/Lon is the common presentation format for this particular coordinate system.
Right now in Sweden the time is 10:41 (it would be great if it was a couple of hours later, then I could say it's 14:41 to demonstrate the 24 hour time format). Yet, in software, I would represent that as time in UTC. Only when presenting to the user would I convert that to the users time zone.
My last name contain the letter "ö". In software, I would use an unicode string internally, then when writing out I would encoded that to utf-8. (20 years ago, I would have used an old character encoding called ISO/IEC 8859-1 or something like that, but you get my point).
For some damn reason I till don't understand, the decimal separator in Sweden is the comma and not the period. Still I would represent numbers internally as an integer or maybe float, and then when printing to to the user would I convert that to "123,4" (123.4) or something like that.
In Sweden, WGS84 is not the only common coordinate system. There are many others: SWEREF and SWEREF TM for example. Yes internally, depending on usecase, I would probably use a representation of WGS84 as reference, then convert that to present to the user...
This is how I think about coordinates.