There are things you can do to make it easier. My phone sends all notifications to my desktop, and I have an app on the phone that creates a notification when it recognises a code in the SMS, so all I need do is double click on the notification (to select the entire "word" that is the code) then paste into the site I am verifying to.
There are also authenticator browser extensions so you do not have to use a phone app for those either.
The software I use for the SMS codes is KDE Connect and SMS code.
We shouldn't have to work installing & maintaining an awkward flow with random software to make buying experience less miserable. This should be fixed by the seller in the first place, where it makes sense and can be fixed easily and reliably.
eBay is responsible whatever partner they are choosing. They knowingly picked PayPal. If the integration is terrible, they can work on this with their partner and maybe find a common way to establish trust.
The seller is motivated to make the buying process as easy, fast, and uncomplicated as possible. This is a direct correlation with how many things they sell, and in response how much money they make.
On the other hand - consumer opinion and regulation forces them to ensure that the buying process is secure, that someone else isn't buying things on your account, that they have proper logging of what goes on, etc.
The seller shouldn't "Fix" the buying experience by removing the security aspects of it. They should fix the buying experience by using modern authentication like passkeys and ensuring that their applications and sites support password managers.
In general I agree, but KDE Connect is not random software and it's fucking awesome, especially if you are a KDE user, for a lot of reasons. The use-case described in the grandparent is just one of many handy things available via KDE Connect
I use GNOME: the gsconnect extension on my laptop, the kdeconnect app on my mobile devices. They can even share data and files between themselves without going through the laptop, ring another one when I lost it somewhere at home, control the media playing on another device or my laptop.
Installing an maintaining is not awkward. Most people seem to install lots of random apps, so why not something useful.
Of the two applications I use for the SMS flow, one is generally useful to have anyway. The authenticator extension or an app is absolutely necessary for this type of 2FA and the alternative to some app is to not use 2FA at all or use SMS authentication.
There are also authenticator browser extensions so you do not have to use a phone app for those either.
The software I use for the SMS codes is KDE Connect and SMS code.