A strength of 15 has a light load limit of 66 pounds, which leaves 16 pounds for other stuff. That's probably the minimum attribute a strength-based fighter would have. Two-handed martial weapons max out at 15 pounds, which is getting quite close. A large shield is 10 (wood) or 15 (steel) pounds, and one-handed martial weapons max out at 6 pounds. (Some of the exotic axes are two pounds heavier.)
So even with strength 15, you can avoid encumbrance. Admittedly, you are going to be worried about how much your potions weigh and a bow or bed roll could easily put you over. Once you're strength is up to 18, the light load limit is now 100 pounds, so you can carry an adamantine ranseur, a cold iron ranseur, a mithral ranseur and still have 20 pounds left over for assorted items. (I picked a ranseur because it's the heaviest two-handed martial weapon.)
Encumbrance could be an issue for full-plate fighters, especially at lower levels if they haven't maxed out their strength. Moving at full speed in full plate doesn't happen until seventh level anyway. By that point, most fighters probably have at least an 18 strength. (15 base, +1 level, +2 item.)