I wouldn't mind if my profile and posts were visible to robots.txt-abiding web spiders such as search engines, but I've come to terms with the notion that social media timelines are transient and, much to my disappointment, posts in them become very hard to find after even a short while, and several users go through the trouble of deleting their own posts. even URLs that search engines might index and show would likely not contain the searched-for terms as posts get pushed to earlier pages.
for more permanent records and presence, I recommend another medium such as a blog over whose URLs and posts you'd have a lot more autonomous control