Earlier quoted context omitted.
They're minor investments practically, and major investments politically. As you say, for many motorists, giving up space on even some roads to cyclists is treated like some sort of war crime. There's very much of attitude of, "we can't just have a majority of the road space -- we need nearly all of it!"
It can be a real winner politically, depending on the electoral boundaries. Roads have such limited throughput that a new bike lane might inconvenience only a few hundred people in cars, while opening up the city to thousands of people on bikes. Once politicians figure out that calculation, it can go very quickly.
A) Cars have a tall stack of interest groups with money to throw around politically. Manufacturers, Dealerships, Gas corporations. lobbying groups including, especially, but not limited to the AAA all have skin in the game and have thrown money at politics. (In general bicycle groups are rarely as organized, rarely have much in the way of profits or income to burn on political favors.)
B) Taxes. Today roads are partly paid for with gas taxes and sometimes vehicle property taxes. A lot of motorists feel so entitled to the roads simply because they see those tax numbers directly on their gas bills and vehicle registration fees and think that they own the roads because they feel like they have the receipts. (Nevermind that there is no state in the US that entirely pays for roads out of such taxes, and the "I paid for it, so I own it" fallacy seems to refuse to ever actually prorate its "ownership" against the actual small percentages any individual contributes to the total budget.)