Technically I think LED is right that sunblock is not absolutely essential. This coming from a Florida native who has seen more than his share of Yankees get themselves seriously hurt when they fail to understand that the southern sun is not the gentle, warm friend they are used to up north.
Frog-belly-white skin can turn beet-red in a shockingly short amount of time. I've carried several people to doctors for 'sun poisoning' and observed the painful debridement of a child's skin required by traumatic sunburn. They essentially peeled off the upper layer of skin using a scalpel and forceps while the poor kid screamed.
Sunscreen may not be absolutely essential because you can get over 90% protection from appropriate clothing. Hat, sunglasses, long-sleeve shirt, long pants are effective.
But, you knew a but was coming, even with appropriate clothing there are gaps. It wasn't a huge deal but I have had a rough time occasionally with burned spots. The sides of the head, lower parts of the ears, tops of the feet and backs of the hands can get painfully burned.
Because of this, and the simple fact that sometimes hats and items of clothing get left behind, or lost, or I simply forget to use them early enough, a little sunscreen is mighty handy to have around.
While a conventional tube or bottle of sunscreen will work the biggest bang for the buck - and so cheap and compact you can buy them in quantity and scatter them among kits, packs, and pockets - are the sunscreen rated lip balms. You can use them on lips, of course, but they can be smeared on ears, the back of hands, top of the feet and make things a lot more comfortable. There is also just enough in a standard lip balm tube to cover a forehead, upper shoulders, back of the neck and nose a couple of times. Enough to get you through a day in reasonable shape if you found yourself without a shirt and hat.
Another case where a little bit of something on you at a critical time can be more effective than huge amounts of material resources that get left behind.