They take all your website traffic and earn while you get nothing!
Don't follow the fad, yes it is only just something that people follow without knowledge of. There is no benefit to you unless all your marketing or advertisers are solely audio based. If you sell products at your website, deliver visual advertising, solicit subscriptions for email newsletter or otherwise, it is counter-productive and a total loss to use stream directories because those users will never get to your place of business. Don't do it! Don't even use apps. Distribute only your domain at any inbound link resource.
You need people coming to your place of business to get your merchandise
The fact is, stream directories are just websites created by someone in a basement (tune in was such) and they just scoured the web and grabbed stream URLs and added to their site for easy content, without the knowledge or approval of the broadcasting site. Overtime they gained popularity and marketed themself for traffic to sell ads. Your audio content which you work hard to produce, becomes their content and you get absolutely none of the revenue they earn. In essence you become a free laborer for someone's site.
The other downside is, many stream directories like tune in, redirect your stream URL through their servers and your provider then see the connection as 1 user when in fact there may be hundreds connected to the URL created by the directory. You never get a real statistic on listener count and not able to produce a valid media kit.
It is also damaging to your brand if you decide to change stream providers, therefore the player at those directories return an error and you look defunct. It is then an excessive time wasting task to log into all those stream directories to change the stream URL.
While you will never be able to block fly-by-night so-called stream directories (there are many) from acquiring your stream URL (it is public to the browser), you should not simply give it up by listing at their website.
Here is an example of chasing away your site visitors.
The owners of this internet radio site is under the delusion that by posting their stream URL at hundreds of stream directories is getting them lots of listeners, but the reality is they are simply sending the very few who hit their site, to someone's website.
When the user gets to those other sites, they will be shown hundreds of similar stations which they can tune into right there at the person's stream directory. Therefore the stream directory get to sell ads and products by using your audio content, and your site that sent the viewers don't make a dime.
Your site traffic gets to the stream directory and never leaves and may ever even tune in to your station because they are presented with a vast choice of related radio. You lose!
The better method for directory listing
There is benefit in using web directories to send or funnel traffic to your site, just not the stream directories. List at standard directory sites where all you submit are your domain, site description, identity image and other pertinent textual data, and viewers have to click your link to get to your site to listen. Don't let them listen to your work at someone else's website.