I love small pocket lights, usually CR2 size and smaller. I have a lot of CR2 type lights and sub-CR2 size ones too. But often I'll EDC an AAA or 10440 light.
Favorite EDC lights
Oveready Peak Eiger mule 10250 in stainless steel or brass
TNC Brass Extreme Micro 15270
4Sevens Mini MLR2 CR2 neutral or cool white
Maratac AAA stainless steel or copper
Olight i3s EOS AAA
Thrunite TiS NW XP-G2 AAA in stainless
Thrunite TiS CW XM-L2 in flamed titanium, modded to 10440 by Vinh
On the keychain is a DQG Fairy 10180 light with the USB charger in my other pocket.
I also love the CR2 size of lights and have a couple on me always, a 47's Titanium CR2 MiNi, and an Aeon.
OP, this is a very good question as flashlights are needed in the daylight hours as well as night.
Also, in my daily carry, I carry a McGizmo Haiku, a Photonfanatic killer and a LaPetite Killer, both bare Ti., as a matching set. After dark, I carry something with some lumens in it! Lately, I have been carrying a Surefire PX2 or P3X both with Moddoo Clips and Triad switches along with an orange paracord lanyard with two Peter Atwood Titanium ribbed beads, a large and a small, on both. I think you need to be able to hold on to the light just walking in the open with it, as well as, if something goes down.
Some think I carry too Many lights, however, that's their problem. I like these things and use them all the time, and at night I feel you need a decent amount of light, for me, I like a good
500-1000 lumens to blind a problem, and get away, with no laws broken.
Flashlights are a great defensive tool, and one of the reasons is you can an be 50' away from some troublemaker and they can't see a thing, they're done for a while. Not to mention it is a huge surprise for them, which they are not used to getting from someone with a leaving a nice car going to the store late at night.
So, carry at least one in the day and add a brighter one for going out at night, or carry several, it's fun! No rules here.