Yes, it's harder to out-compete fossil projects that have already been built, already paid off their capital costs, and incur just operational costs going forward. Some of those fossil projects (like Saudi oil fields that cost only $10/barrel) are not going to be economically forced into early retirement by any foreseeable lower-emissions energy source.
Note that there is also quite a bit of already-built fossil capacity that can be retired early by economic pressures. Not every big fossil project has operational costs as low as Saudi oil.
For example, the Navajo Generating Station is the largest American coal plant west of the Mississippi River. It was built in the 1970s. It has a stable, low cost for coal since it is supplied by the nearby dedicated Kayenta Mine. Just a few years ago it was planned to run until 2044. But the falling costs of gas and renewables have made it economically uncompetitive. It's now going to close at the end of 2019, 25 years early:
https://www.azcentral.com/story/money/business/energy/2017/0...
I agree on the broader point that fossil fuel emissions won't be curbed quickly without active regulator intervention. Since that intervention may arrive late-or-never in different nations, it's one of the reasons that I believe active carbon dioxide removal measures will be necessary in addition to emissions reduction efforts.