The games UI/Tutorial doesn't explain this as far as I could tell,
but if you're in your ship and you open the scanner, you can look at whatever planet you want to go to, then press E.
After that it will give you
a prompt to travel by holding R, at which point you will start to fly towards that planet, the same thing goes for landing on a planet too.
Its not seamless but I've seen a lot of complaints about looking at the map all the time, this effectively makes it so you only need to open the map if you need to land somewhere precise, or to grav jump to another system.
UPDATE: Ok turns out
if you have a mission selected you can actually jump to a different system using the exact same method, meaning its entirely possible to travel through space without having to open the menu every time. You'd only have to do it when you want to change missions to swap systems for example, honestly its quite immersive overall.
EDIT: Adding a link showcasing how it works cause theres still a lot of questions