GH-47721: [C++][FlightRPC] Revert #48050 #4025

Job	Run time
check-labels / Check labels	26s
matrix.title	-1s
JNI macOS	-1s
ODBC	-1s
JNI ${{ matrix.platform.runs-on }} ${{ matrix.platform.arch }}	-1s
ARM64 Windows 11 MSVC	-1s
report-extra-cpp	0s
	21s

Provide feedback