Yeah, you could add a rear brake easily. The front would probably require drilling. Can’t tell for certain given that angle.
The thinking (I generally disagree with) with children is to transition them from sidewalk bikes to real bikes is with a coaster brake and a rear handbrake. Many adults are afraid of the front brake, which is a shame, since it’s so much more essential.
If it were my wife I probably would add a brake, unless I knew the bike would never leave the boardwalk. Did I ever tell you about Charity Horn? She lost her life descending a hill when her chain derailed. She only had one brake, a Bendix coaster.
You can zip tie the rear brake cable housing. Or get fancy bolt on cable stops for interrupted cable housing, which is better.
Still, drilling a hole is no great shakes.