Admittedly, for an enhanced "Hornblower Effect" regular shuttle departures and arrivals would have added a maritime touch to the show, and had they constructed the scripts to have the shuttle's travel time match a commercial break / slot events would have occurred in real time.
But from a practical point of view you would have just seen people entering or exiting a prop (shuttlecraft) with no funky special effects involved. I'm afraid that would have rather gotten stale over extended periods of time.
The transporter room was a unique trademark of Star Trek and I think audiences quickly got the feel that once our protagonists embarked the transport chamber they were going somewhere (in real time).
On the bright side the shuttlebay scenes became a special and rare event to be appreciated.