It’s possible, but it’s unlikely to be worth the astronomical cost. I don’t think you realize just how much more enormous such a job would be. Aside from deepening the existing cut, you would also no longer have the benefit of cutting the distance by using Lake Gatun, so you would have 50 miles of excavation instead of 13. You would have to cut a diversion channel so that the Chagres River wouldn’t flood the canal during torrential rains during the rainy season. The rock in the area is unstable (in the early years the Culebra Cut was often blocked by landslides), so you have to excavate a good distance out from the channel to get a stable slope. Then you have the environmental problems produced by allowing the faunas of the Pacific and Caribbean to mix. And on top of that, you’ll still need locks anyway, since the tides of the Pacific reach almost 18 feet and are out of sync with the two foot tides of the Caribbean.
And one more thing: all that expense and effort would only amount to saving a few hours on each passage by eliminating a few of the lockages. A transit through the Canal only takes about 8 hours anyway. Saving a few hours out of a voyage of several weeks hardly seems worth it.
When the French tried to build the canal, the land was part of Columbia. The USA helped the Panamanians revolt and thus the new (and grateful) country was happy to cede a nice big swath through. The Canal Zone was an American Territory until the late 1970s. I was able to watch the USS Iowa transit the Pacific side locks back in the day, frappin’ amazing.
I wouldn’t say they were happy to cede the land. There was a lot of chicanery involved on the part of the Frenchman Philippe Bunau-Varilla, who was appointed Ambassador to the US by the new government but promptly sold out Panamanian interests.
Panama ratified the new treaty mainly because the US threatened to withdraw support and allow Colombia to take over again.