Sometimes you want to measure breakaway torque. This can tell you if a fastener has started to loosen due to vibration, or was over-torqued and the bolt/stud may have stretched or weakened, or the fastener was cross-threaded and need to be replaced. Note that breakaway torque values will often be higher than the stated torque spec, as the breakaway torque measures static torque (the fastener is not moving), while the tightening torque is a dynamic value (because the fastener is still moving).
If you fear that the nut or bolt are seized, and you don't want to damage the part it's attached to with excessive force, you would use a torque wrench to warn you that you are exceeding the torque which might result in breaking the bolt/stud or otherwise damaging the fastener.
It's also useful if you know the fastener will take the force, but for whatever reason you have a substandard tool. For instance I recently damaged a specialty torx bit when removing seatbelt bolts. If I had used a torque wrench I would have stopped applying force and used additional methods to loosen the bolt before reapplying the force.
Another, somewhat different consideration, is that "clockwise only" torque wrenches are not suitable for left-hand threads – in case that matters to you. Of course tightening a left-hand thread is the same as loosening a right-hand one. Beam type (scale and pointer) torque wrenches are reliable and inexpensive and all of the ones I've seen will work in either direction.
I've been wrestling with this issue regarding having a decent tire removal tool/basic car repair tool in the car because the original wrench to remove the lug nuts is too short and mechanics notoriously tighten the things too much. Presently I have a Torque wrench and a long socket ratcheting bar in the car, but I notice that Aldi has decent torque wrenches on sale now (2018/10, Germany) for about USD 22.00 including tax. The kits come with three sockets and an extension in a plastic storage box. At that price one can have one torque wrench for tightening and one for loosening. The advantage over a breaker bar is the socket ratcheting function. All one has to do is tighten the torque wrench up to the highest level and that is still twice the torque of just about every bolt on the car one would want to loosen. Of course one has to remember to loosen the torque wrench at the end. I know, these torque wrenches are not the same as the big name brands, but after 20 years of tightening bolts one really doesn’t need to pay over USD 150 to just tighten a few bolts now and then.