Shoes stretch out over the course of normal use. I like no more than a c*nt hair of space before the big toe.
Natural materials stretch and break in. Synthetic materials don’t. Do you wear leather running shoes?
Well first of all GFY! Second, I’ve never had a pair of running shoes that didn’t stretch out by 20-30 miles(and typically keep stretching). Unless you like your foot swimming around in the shoe, no point in buying giant clown shoes. Snug with just a tad up front is the way to go and keep in mind your shoes will stretch a little to a lot!
Half sizes? I thought they only have those in children’s sizes. I wear 13/14 but have never seen a 13.5.
2. The swelling thing. I can't think of a single serious runner that believes their foot somehow elongates a full inch during the course of a training run, thereby causing them to suddenly hit the front of their shoe (the toeguard). However, you know what does often happen? A foot that feels quite snug in the store, can suddenly start feeling a bit tighter after an hour of pounding the pavement. That one spot that may or may not have felt tight in the store, actually begins to hurt. Now think about the shape of a shoe, and remember that the front of the shoe that tapers towards the toe is easily the most narrow. Keeping that foot from being crammed all the way into that area makes it less likely for the shoe to start hurting on the first long run and come back to the store as a return.
This is why the best time to try on shoes is right after practice; your feet will be at their largest from any possible swelling, and you can select the right size (regardless of what it actually is in comparison to other shoes you wear).
I think it depends as well on when you get your feet measured. If you get your feet measured when it's cold, you are really cold, it's first thing in the morning that is one thing. For running shoes it may be hot, you may be hot, it may be in the afternoon or evening and you may have been on your feet for hours. So I would not be massively surprised if there was some kind of sizing discrepancy there. But I think the size up thing is often because it is better to have a running shoe that is slightly too large than one that is slightly too tight!