My big issue with JWTs: securing images. With cookies, a browser attaches the cookie on the image request. With JWT, a browser does not send it with the request. Cookies are far easier in this case.
If the token is only good for one use or for a short period of time (minutes not hours) it's probably fine. I've used them in URL's for invite links. One time use that expire after a short amount of time. Probably not perfect for high security applications like banks or health care but for most applications it's fine.
Sure it does, just put the JWT in the cookie ;)