Yep, the TVA and other programs did help us in rural areas... as did various other programs / legislation that helped push the PHONE out to rural areas.
DO NOTE Though, that by 1939, the REA / TVA had only provided electricity to 25% of rural households... only a 15% improvement, or it just over doubled the number of households.
HOWEVER, then have never revoked or cancelled the "tax / fee" that the power / phone companies were allowed / forced to CHARGE to fund those programs !! So we are STILL paying for programs that ended DECADES ago... they now just line the corporate pockets !!
I live in a very rural area, and it takes almost FOREVER to get PG&E or AT&T to provide service out here !! AT&T still hasn't gotten us cell-coverage (I did it by building my OWN cell antenna over a RF Broadband service built by another friend !!) and PG&E frequently drops us off the grid so the "City dwellers" can keep their power !!
We now have solar and wind on the ranch to provide us all OUR power... but now the power companies don't want to PAY for the extra power we push back onto the grid !!