On the one hand, yeah, and I'm sure there were plenty of people cursing up a storm about the difficulty of getting at the headlamp switch on these cars, especially given the crummy quality of parts Chrysler were accepting at the time from suppliers (supplier-kickback scheme at Chrysler at the time — CEO eventually lost his job over it, etc).
On the other hand, no cars are designed, engineered, or intended to last anywhere near as long as the one you're presently cursing up a storm at.
While you're in the neighbourhood of the headlight switch: On pre-1968 vehicles (with a few exceptions not including your car), the parking lamps do not remain lit when you turn on the headlamps. For 1968, this was changed so the parkers stay lit with the headlamps for safety (in case of a headlight burnout you still have at least some visible light on the burned out side of the car). This is easy to retrofit: remove the headlamp switch and unplug its multi-wire connector. Put a short piece of 18ga wire between from the "P" to the "R" terminals on the headlamp switch body, right down at the base of those terminals. Make sure the ends of the jumper are neatly tucked so they won't touch any adjacent terminals. Solder if you like. Then push the connector back onto the switch, on top of your new jumper wire which won't get in the way, and reinstall the headlamp switch. This will emulate the wiring setup of '68 and later cars that keep the parking lamps lit with the headlamps on.
Also while you're in that neighbourhood, heed: there is minimal electrical protection in the '60-'61 cars. A few individual circuits are protected by inline fuses, but that's about it, and there is no main circuit protection (fusible link). Adding a good deal more circuit protection is a very fine idea, sooner rather than later if you want to keep the car.
This thread has resources and pointers for upgrades.
If you are modern you have fitted the radio speakers in your rear parcel shelf. 