You can set your iPhone to secure erase after 10 failed pass-code attempts.

In addition you can use long alphanumeric pass codes and even the default new passcode option is being increased to 6 digits (though you can choose a 4 digit option).

This renders the brute force option pretty useless. Which I'm fine with, I don't want to make things easier for crooks or identity thieves.

There are ways around that still http://techcrunch.com/2015/03/19/iphone-bruteforce-pin/

In this case they cut the power to the device before it can write to memory the failed attempt (IIRC) allowing them to keep trying over and over (with a small delay for the phone to restart every 9 tries).

Would that work against a determined opponent with physical access?

Unless the iPhone has some fairly high-grade encryption hardware I suspect you can just do fun things like copy the (encrypted) storage/key to brute-force it without the safety mechanisms kicking in.

It does have some pretty fancy encryption hardware and Apple seems to have made it very difficult to do even with physical access.

David Schultz wrote a pretty comprehensive article about it:

http://www.darthnull.org/2014/10/06/ios-encryption

After a certain number of failed attempts, newer devices lock themselves.

According to this writeup, that may be worked around by resetting the device after every few attempts: http://www.zdziarski.com/blog/?p=5106 (penultimate paragraph)

Exactly! Most of the time they are 4 digits. Also what about finger prints on the phones?