Linen loses about 20-30% of its wrinkle resistance once it hits the washing machine, so you're fighting uphill from the start. The real trick most people miss is that you don't actually want to fully dry linen - that's when the fibers set into permanent creases. What works better is pulling it out while it's still damp (like 60-70% dry) and hanging it on a proper hanger immediately. Smooth it down with your hands for maybe 30 seconds, making sure seams and collar are straight, then let air circulation finish the job. The moisture helps the fibers relax back to their original state instead of locking wrinkles in place.
Where people go wrong is thinking a steamer fixes everything after the fact. Steamers definitely help with stubborn creases, but they're more of a maintenance tool than a solution - you're still spending 10 minutes on a shirt that way. The preventative approach actually saves time. Fold or hang linen immediately after that hand-smoothing stage, and store it loosely so air can circulate around it. I've found that linen that's been sitting bunched up in a drawer for a week will wrinkle way more than something that's been hanging freely.
One more thing - accept that linen will never look "crisp" in the traditional sense. It'll look relaxed and worn-in, which is kind of the whole point of wearing it. Some wrinkles are just part of the aesthetic. If you genuinely need razor-sharp creases, linen probably isn't your fabric anyway.