It may be a cycling jacket, but maybe not a cycling jacket for the typical road cyclist. Might be more for the touring cyclist which use road bikes too, and is another sub-forum.
If you don't like bulky things shoved into your jersey pockets then look at all the bag options for handle bars, top tubes, saddles and even panniers..... but by that time, you are well into the other sub-forum type riding.
It's not a best dressed contest or dash down the runway for lulu lemon outfits. We won't care if you roll it up and stuff it inside the front or back of your jersey.