As you use higher gears in the transmission the clutch will see higher torque, as feedback from the tires through the gearbox. This means the clutch absolutely has to slip some while engaging in the higher gears. If the tires could not slip, and the clutch could not slip, then you would get instant deceleration of the flywheel, which would break the crankshaft from internal engine inertia. We know that doesn't happen.

The clutch has two functions. First is the common function of disengaging to allow engine and propshaft to turn at different (not synchronized) speed during shifting. Second is the function of intentional slippage while transmitting torque to dissipate energy and bring the engine flywheel and gearbox input shaft back into synchronized speed. Any clutch, regardless of size or design, will handle that first function properly.

The concern then is to match the clutch design to perform the second function in an acceptable (or desirable) manner. This function can vary depending on the end use, and may in fact be a matter of personal preference. For street use you may like a "soft" clutch that slips more and engages gently for a smooth start, no jerk, and does not spin the tires or kill the engine. For competition use where the clutch may be regularly used in a more severe manner, you may want a stronger clutch to engage quicker so as to minimize wear on the clutch. As noted before, the torque capacity of the clutch must be minimally somewhat higher than the engine output torque. The question then is, how much higher is good?

The first goal here may be to have enough clutch torque to be able to spin the tires in 1st without slipping. Most street cars can do that, so if you rev the engine and pop the clutch in 1st gear it will spin the tires (at least a little) and give you a good launch without burning up the clutch. From there on through various shifting functions, as long as you don't abuse it too much that clutch will not slip much and may last a very long time.

A race car with close ratio gearbox may effectively have no 1st gear, and final drive ratio may be selected to run engine near top speed (peak power) on the fastest sections of the track. Given a short enough track and high enough final drive ratio, the top gear overall may be about like 3rd gear in a street car. I fondly refer to this practice as having three 2nd gears and one 3rd gear. A stock clutch might not be able to spin the wheels in the lowest gear, and a race engine may have very little torque below 2000 rpm. The stock clutch may have to slip continuously on startup until the car reaches at least 10 mph ground speed. In this case the clutch may need to be quite a lot stronger to provide enough torque to spin the tires in 1st gear. So you might want (or need) to install a competition clutch for increased clutch torque.

When upgrading the engine power, you don't necessarily need to worry much about clutch capacity just because of increased engine power. When you increase engine power without increasing displacement, most of the improvement comes by improved breathing to increase torque at higher engine speed. So you get more net power at high speed, but maybe not much more peak torque. And if you use a lightened flywheel, you may even see less torque for the clutch to handle. The greater concern for the clutch is related to the overall gear reduction ratio (especially in low gear), and the amount of grip you can get from the tires. Taller gearing for low gear may beg for a little stronger clutch. Stickier tires for competition use may demand a stronger clutch.

Another reason for upgrading the clutch is for competition use where you might make a regular habit of power shifting. That means standing on the throttle for best acceleration while the clutch is still slipping immediately after a shift, and in particular maintaining high engine speed during the shift to retain maximum energy in the flywheel. In this case the clutch will often be slipping significantly during shifting to dissipate the flywheel energy and some additional engine energy at full throttle. This could overheat the clutch, or it could cause unacceptably rapid wear on the clutch disk. In this case installing a stronger clutch can reduce the slippage (while the engine is slowing quickly to match propshaft speed), transmitting more energy to the wheels, dumping less heat into the clutch, and reducing clutch wear. The end result is desirable, getting quicker lap times and reducing maintenance cost. While this is a noble goal for a race car, for a street machine it may give undesirable high pedal pressure, and also harsh clutch take up which may either kill the engine with a sudden jerk or spin the tires on startup when you don't need it.

This stuff is all a bit of a compromise. You may want a soft clutch for street use and a stronger clutch for competition. When you use the car for both street and competition, it quickly dawns on you that the clutch is not adjustable, and you have to decide which side you will compromise to favor the other. If you are determined to do your very best at competition, then you may settle for a stiff leg and having to finesse the harsh clutch on the street. If the competition is occasional and mostly for fun, maybe not so serious, then you might favor the stock clutch and just try not to beat it to death during competition.