I'd consider myself proficient with using a gaiwan now, but I wasn't for the first few years of my tea journey. I was scared of them.
That's not going to filter the tea properly. That looks uncomfortable to use. I'm gonna burn myself!
At first, I used tea infusers that sit in your cup. These bothered me for a few reasons: some tea types don't expand and steep well in a confined space; they clogged constantly; and they can be annoying to clean.
I then took my first baby step towards gaiwans - with an "easy" gaiwan. It was a nicer experience, but still had some of the same issues: it tended to clog and was annoying to clean. It has a lip that is difficult to clean under. And it actually lets quite a bit of tea bits through.
Similar to this one:

After a few years, I got my first gaiwan for cheap, and I'm so glad I did! It was just easier. You can keep the lid mostly closed and it somehow filters tea bits better than my "easy" gaiwan. It's soooo easy to clean. Now, I do actually use a filter sometimes to catch fine tea dust, but I don't actually need to.
I'm sure gaiwans are synonymous with loose leaf tea for many people, but they aren't common where I am in the US. So for anyone who hasn't tried one, I say give it a try!
-- PS - One cool looking kind of teaware I have yet to try is a shiboridashi. This looks like a better version of my "easy" gaiwan:

I have a gaiwan but I don't really use it that much anymore. I only use it if I'm in a specific mood for it and I'm making sheng puer.
I started off with an "easy gaiwan" too, but had pretty much the same experience as you.
For most other teas I have a small 150ml porcelain teapot from Jingdezhen (I'm lucky to have a local teashop which imports tea & accessories directly from sources!). I pour the tea into a pitcher from the pot and use a small cup to drink it.
For japanese green tea I have a Kyusu because aesthetics are important! :D it's a bit difficult to clean though, but not too bad.
If there's more people than just me drinking the tea, I'll just use one of those large western-style teapots and normal cups. I find that people get weirder out wjen I offer them tea from a cup smaller than a tablespoon. 😅
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