Personally, I only ever ask people to solve coding/problem-solving questions live. The best experience IMO is when we talk through the problem together, since this approximates what collaborating with this person on real tasks will be like - not very well at all, but about as well as one can do in the amount of time available for a live interview.
However, I do understand where the offline exercise idea comes from - it's not necessarily about lack of respect for candidates' time, but is generally done with the best of intentions in response to feedback, because candidates complain that the interview technical exercise scenario is needlessly artificial: in a live interview candidates do not usually have easy access to their usual tools or Google/Stackoverflow, and many feel pressure and panic from having to code/problemsolve live while someone is watching and feel they would do better if left alone to do the same thing for the same length of time.
Given the incredibly strong feelings either way, perhaps it might not be a terrible idea to let people choose which approach they prefer; but I've never seen any company's hiring do that, though, thinking about it, there really is no good reason why not (provided I still get to talk through the results of the offline exercise with the candidate during the live bit!)
I think this is a good analysis of where the offline idea started from, but in my experience the majority of interviewers who want you to do a "take home" thing are asking you to sign up for a multiple-hour mess of a project. That's where the lack of respect comes from, and the lack of acknowledgment of the market--most people you want to hire are already employed, after all, and time pressure from life is a thing.
Making it an option for somebody who would rather wouldn't be bad, but yeah, as you say, nobody's learning a lot about the other people that way, and they're probably more important.
(The OP's card deck problem is just faintly ridiculous and a bad allocation of the candidate's time, and I assume there are more hoops to jump through afterwards.)
However, I do understand where the offline exercise idea comes from - it's not necessarily about lack of respect for candidates' time, but is generally done with the best of intentions in response to feedback, because candidates complain that the interview technical exercise scenario is needlessly artificial: in a live interview candidates do not usually have easy access to their usual tools or Google/Stackoverflow, and many feel pressure and panic from having to code/problemsolve live while someone is watching and feel they would do better if left alone to do the same thing for the same length of time.
Given the incredibly strong feelings either way, perhaps it might not be a terrible idea to let people choose which approach they prefer; but I've never seen any company's hiring do that, though, thinking about it, there really is no good reason why not (provided I still get to talk through the results of the offline exercise with the candidate during the live bit!)