Hello Ken,
I'm glad I asked the question. Your absence on the Forum had me worried. Your answer is certainly logical but I can understand how some players may question a bet that is larger than the pot at the time of their "pot size bet."
Proper rake procedures for cash games might vary but, I like to teach dealers to wait for a betting round to be complete, burn and turn, sweep the bets into the pot, start the action, and then take the rake. The end result, will allow the dealer to take the proper %(or amount), before the next round of betting. Counting the pot after the final betting round, and taking the rake while pushing the pot to the winner, is poor dealer practice and not recommended.
Don't want to get too far off the subject, just trying to establish an easy way to justify the larger bet than the amount in the pot at the precise time the "pot size" wager is announced.
Taking the rake on a "time session" as opposed to a flat percentage with a specific max take-out, would never affect the size of the pot. Might be a good solution for pot limit.