Compact cameras (under $500) usually have great macro lenses too, though you miss the flexibility of being able to change the lens. I've owned for quite a while a Micro Four Thirds camera from Olympus and that's a very good spot to be a hobbyist: not too expensive, but can do "pro things" like changing lenses, shoots raw, has a horseshoe socket, etc. Of course, the quality is not the same as a full frame camera, but then again, I'm not a pro :)
Yes, and Sony has been really impressive with their cameras lately. It looks like finally Canon and Nikon woke up and start trying to match their (unfortunately for me, Olympus decided to sell their camera business? Did somebody buy them yet?).
The thing about larger sensors, for those that aren't aware, is that they produce much better quality images because each pixel is larger, and can gather more light. More light equals a stronger signal, in a noisy ambient.
I sometimes try astrophotography because it lets me combine my photography hobby with my programming passion, and I end up writing my own processing pipelines. With a compact camera, I could get the ghost of one of the brightest galaxies in the sky (Centaurus A in the southern hemisphere). With the MFT camera, using the included kit lens I got a little bit of detail, but it was just a few pixels wide. Switch on to a vintage lens I got for ~15 dollars, and I managed to get the galaxy and quite some detail. Not the same as a telescope image, but very impressive for a 1970's lens on a small camera!
And the noise levels aren't even comparable. My old compact camera was Noisy with a capital N. Of course I didn't realize it when I bought it, but it was[0]. I see the same on phone cameras (the sensors are about the same size now). The MFT even on ISO 25600 (highest it goes to) isn't as noisy as the compact camera was at 3200.
Most phones will cover that with a lot of computation, and that's fine for a small screen. But load your pictures on a large monitor and you'll start seeing the details and differences. However (and it has been said everywhere in the comments) phones are usually way more convenient because you always have it with you.
[0] For reference, some 12 years ago I bought a Canon G12, then a G16, and then moved on to a Olympus OMD E10. On every change I got far better quality at about the same camera size, though the olympus is slightly more bulky, and you have to factor in the lens too.
