Substitute Question
 

NFHS Rules:

Shooting foul on B1. A1 gets two throws.
Team A coach calls a 60-second time out. Granted.
After the first horn sounds, A7 reports to the table. Told to wait -- too late to enter.
After the first free-throw by A1, horn sounds.
Is A7 allowed to enter?

No reason (or rule) not to let him in after the first FT.

Restrictions on a sub entering the game are well-defined and few in number.

This isn't one of the listed times, so let the sub in.

Restrictions on a sub entering the game are well-defined and few in number.

This isn't one of the listed times, so let the sub in.

Is it safe to say,
 

that the restriction against a sub entering 'late' out of a time out (3-1 a)is strictly a measure to ensure a timely restart of the game, and not allow a team to cause extra delay with substitutions?

Unlike 'sit a tick' rule for a substituted player which is a restriction on a player returning, it seems the intent of this rule is timely restart, and nothing more.

IT's that and giving a team a chance to discuss tactics in the game based on who is in the game from the other team.

Clearly you work HS games in CA. ;)