I agree with this, but I don't think a probation period is the solution. IMO it's actually worse than the standard hiring process.

Something I didn't realize earlier is that there's another disadvantage to the probation period: competition. Having several candidates working side-by-side that know only one of them is going to stay will create immense competition. They will be working side-by-side since they're all there for the same job in the same team, so you can't split them up and put them in different teams.

I see several problems with a competition like this:

1. Some of the candidates will do everything they can to make the others look bad, instead of making themselves look good. Anybody skilled enough to get this far with such deceptive skills will have mastered them well enough such that I'll be hard to find out.
2. This competition creates unnecessary stress. They will need to work harder than the expected norm since they each want to show they're best. Thus, the probation doesn't show the candidates what the actual working atmosphere is.
3. I personally feel that internal competition in a team is a bad thing. I think that it prevents team bonding and the formation of trust between your colleagues. Even if this is only the case between the candidates, the competition will create noticeable tension, which can influence the (productivity of) the team.

The standard interviewing question doesn't have this competition problem. Candidates shouldn't ever encounter each other. Furthermore, one is able to make sure the interview is equally hard for each candidate, making sure selection is 'fair'.

If your concern is mainly about the on the spot logic questions and whiteboard coding, then this is fixed with take-home assignments or putting them in a room with an assignment, a laptop, an IDE and internet for an afternoon. Both assess the quality of the solution and their explanation of it afterwards. If they're informed up front that they should explain their solution/approach, they should be able to do this since what I just described is in part the process of documenting.

If your main concern is the company missing out on a great developer, then I'd like to emphasize point 5 I showed: make sure the interviewer has social skills and patience. Someone with proper social skills is also able to interact with introverts, not just with other 'more socially equipped people'. Combine this with patience and the interviewer needs to be able to see past mere introvert behavior.