I don't know what their preferred phone was at the time, but they were unwilling to go through the same effort for the Secretary of State, instead offering her a choice of non-BlackBerry phones.

This is likely because his modified BlackBerry was a one-off project suited to his security requirements.

My understanding is that internal hardware was removed/shielded, and I assume software modifications were made as well, like only connecting to specific cellular base stations (such as the one in his official vehicle).

Which is absurd, a SOS is mobile far more than a President by nature.

I think the importance of this cannot be understated. The Secretary of State is a nexus of not only extremely sensitive information, but of extremely sensitive information in motion which is also in overseas locations more often than not. If I were into tradecraft, I'd be much more likely to target the Secretary of State than the President for access to (relevant, valuable) sensitive information.

BlackBerry was probably the closest, and I expect they already knew what modifications to make.