No current console can really consistantly pump out smooth frame rates at 4K when it comes graphically advanced games... not even the souped up pro versions of the Playstation & Xbox (although they do offer improved performance at 4K). As you mention frame rate is massively important in racing games especially when you become competitive and are using hardware such as a wheel and pedals... generally speaking the lower the frame rate the more input lag you'll experience when turning the wheel (or moving the thumbstick). The majority of people won't notice it but it's always there and ultimately it will be negatively effecting your speed if you're half decent and able to put in consistent laps.
On top of this Televisions traditionally produce more input lag than monitors, running at low frame rates on a television is basically the worst conditions for racing games.
The ideal setup for GT Sport would be to have your Playstation plugged into a monitor (1440p or 1080p), you would get better frame rates, smoother game play and less input lag. Obviously though a big perk to console gaming is being able to sit on your sofa and play through a TV... so maybe a standard 1080p TV would be better in your situation. The image quality would be worse due to the lower resolution but the gameplay would be a lot smoother which is by far the most important thing for racing games.