I'll play the devil's advocate and say that you absolutely do need your own website/mailing list/CRM/etc because those are the only platforms you can truly own your customer data and engage directly with your customers without the filter of an intermediary stepping in to define the rules of engagement.
Don't get me wrong, I love the ease of using someone else's STR platform as much as everyone else. AirBnB's done a great job using VC money to build a better VRBO, but basing an entire STR business on one platform is volunteering to play by someone else's rules: rules that are aligned to very different objectives than the ones each of us have as owners.
More importantly, as we've seen with Google, Facebook, and virtually every other "free" platform, it's only free until you're hooked, after that it's pay to play. I've seen this on my own STR in just watching the search rank change once I turn on Instant Booking or tweak settings to be more in line with what the latest "feature" that AirBnB has a vested interest in promoting. Smart pricing tools are perhaps the best indicator of this: leveraging huge pricing data sets to show how AirBnB's own "smart pricing" as primarily a tool to allow AirBnB a competitive advantage against hotels vs maximizing long term profits of STR owners.
Depending exclusively on someone else's system isn't growing your asset, it is turning what you own into an asset for someone else with much less skin in the game.
Seth Godin had a far more articulate explanation, using the analog of "share cropping" for modern social media and platforms. I'll even save you the trouble of listening to the whole episode and cut right to specific section of the podcast episode. It's an insightful couple minutes of audio from a perspective we don't hear enough from in the age of social everything:
https://overcast.fm/+L0YU4_L80/17:53
How to do it? Lots of great ideas already posted here. Tons of options on WordPress or templated website builders out there for the DIYers or maybe you just invest the $1k you would have wasted chasing ever-rising FB ads over the next couple years and have a developer build it for you. Either way, the goal is investing in a system that allows you full ownership over customer data beyond the platform so you can actually build a business around your customers, not customers that look like yours but are really someone else's.
In my own STRs, I view each of the major platforms as basic lead generation only. Once first-time customers become guests, it's my job to ensure they come back by "owning the channel" and keeping folks out of AirBnB's shopping aisles to get picked off my another, cheaper option. None of that's easy so I welcome others' thoughts on what's worked best for you in getting repeat customers to come back again and again.