Sometimes controlling depth of field is most important, so you'll be in aperture priority. Sometimes controlling motion is most important, so you'll be in shutter priority - a photo of a moving car or a waterfall looks very different at 1/125 compared to 1/1000.
Manual is less frequently used today, but it's still vitally important. There are plenty of creative applications where you want or need full control over the exposure triangle. Modern autoexposure systems work incredibly well, but they'll still fail catastrophically in some complex lighting situations and still make decisions that aren't in line with your creative intent.
Big strobes aren't a studio-only tool and are often used in the field for fashion, product and architecture photography; TTL strobe systems are available, but you won't always have (or want to use) TTL metering. I've often gone fully manual even with just a speedlite, because any sort of automatic control introduces an unpredictable variable. Underwater photographers nearly always use manual exposure, because AE and AWB systems can't cope with underwater conditions. There's still an important place for bulb exposure, particularly in ultra-low-light and lightpainting situations.
More broadly, learning to shoot in fully manual mode is IMO essential if you want to fully understand exposure. I still highly recommend shooting a few dozen rolls of film early in your photography career, because it breaks your reliance on automation and the shoot-review-reshoot loop. Autoexposure is an extremely useful tool, but your skills will always be severely limited if you depend on it totally. Learning to use the zone system and estimate exposure in your head is hugely empowering and liberating, even if you go on to shoot predominantly using AE.