The real world lineage is in the keeping of the name. Some names get recycled for a while, then fade; some endure. But you're right that the Trek idea of passing those names to better ships isn't real world practice.
As for the flagship thing, that's fanon and writer confusion about what a flagship is. Yes, the D is referred to as such, in the meaning of Starfleet's prime showboat, but it doesn't mean it's an admiral's command ship. Essentially, Pike seems to have commanded a Galaxy Exploration cruiser, Kirk commanded an Independent Duty cruiser (meaning he was available to any command of Starfleet, but patrolled wherever he pleased on his own initiative until such a command called on his services), and Picard did the same with a bigger, showier ship where "explorer" replaced "cruiser" as the designation. So fans and writers tend to assume that at least the 1701-A had that status, and that it must
be passed on to any ship named Enterprise-any bloody letter.
My first exposure to wikipedia was reading the article on the USN carrier, and some idiot had edited it to say that after the ship's heroics in WWII, the US Navy had made a regulation declaring that there would always be an Enterprise, and that it would be the flagship of the navy!
On the Fleet Captain issue, I personally like it. One possible justification is that, like Commodore, it no longer refers to an actual rank, but rather to a position. So a Fleet Captain might be what we call a Tycom today (Type Commander). A Tycom doesn't command a ship. They manage all ships of a class. They make the decisions on what changes may be made, when yard periods are needed, what maintenance is required, what materials may be used, etc. If a captain wants a new door in a given location, and the old door replaced with a bulkhead, the Tycom has to approve it, or he's not allowed to make the change. So a captain who gets a Tycom billet is referred to as a Fleet Captain, just as a captain in charge of a squadron is a Commodore.
In my own fiction, I do use the rank as an often bypassed intermediary to flag rank - occasionally someone is made a fleet captain to improve their seniority over their fellows, more often they get it as a sign that they're too much of a cowboy to ever be allowed to make flag rank. Otherwise, the majority of captains either retire or become admirals without ever stopping off as fleet captains. But that's just my take on it.