What are the benefits of going with an untethered wall charger?
Aesthetics - if that is important then "retractable" might be best for "tidy" and also "convenient".
People knicking your juice when you aren't there (I'm doubtful ... parked outside your house for hours on end!). Isolator switch perhaps? But if that is indoors then have to go indoors to turn on/off.
Isn’t the primary reason for a wall charger convenience and therefore a readily available cable to connect to the car?
That's my view too. I reckon it would be a right hassle to have to fish out the cable and connect it each time ... particularly putting it away again when raining. Also Wear and Tear on the "socket" shoving the Plug in and out each time too (its not like a 13 AMP plug, these things are reasonably chunky, but the socket doesn't have to be flimsy of course ... but "cheap" usually is ...)
One "cheap" route is a Commando socket and EVSE cable, procured from cheapest source. Some things that need to be done to make this "pukka" ... such as a Commando Socket that has integral lock, so cable cannot be removed when power is on ... but for a DIY route, and with suitable care, I reckon that would be the cheapest route. This is best suited to garage installation, rather than exterior ... and even then the whole question of the right sort of trip switches, earthing stakes, and all that stuff comes into play ...
Personally I'd prefer to have a Sparky do it in order that all the right decisions are taken. I used the one recommended by Tesla (actually the second one they recommended ... the first one had gone bust
... bare in mind that way back then very few Tesla sales, so Tesla just unaware that out in the sticks where I live their Approved Installed was no more ...), but I do have a friendly sparky who would be perfectly competent to install a non-OLEV Wall Charger, and would certainly only charge me T&M, let me route the cable myself / dig trenches / anything extra needed like that.