practical applications
In my opinion, the need to create handspun yarns is a perfectly practical real-life application. It's understandable, though if that's not the case for you. Here are some -- but by no means all -- other situations where we can benefit from tensile strength.
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(Be warned: I feel weird using photos of other people, so these are all my photos, despite the fact that not all of these are really... my thing.)
CLOTHING FABRIC
There are a lot of considerations to be had when determining what yarn to use for clothing. Tensile strength is not always the top priority -- sometimes drape (modulus) is, like in the pictured shawl/scarf, which features unplied yarns. On the other hand, the sweater, which gets a lot of wear, is made from 4-ply sock yarn, to give it extra stability.
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Commercial knitwear comes in both single and plied yarns. Oftentimes, you will find that pieces made from singles fall apart more easily.
CLOTHING SEAMS
Over the years, people have used various strategies in order to increase the strength of threads for sewing clothing. This is because seams take a lot of stress -- they are responsible for keeping garments together and holding them up. Historically, one strategy used to strengthen thread was to coat it with beeswax. Nowadays, much of our thread is 3-ply. The strength of the thread is important to ensure that it does not snap either during the life of the garment or as it goes through the electric sewing machine.
SUTURES
Stitching isn't only used in clothes -- it's also used in medicine. Whether for small tests like biopsies or larger surgeries like amputations or wounds from accidents, sutures can be used to hold the wound shut and ensure that it heals nicely.
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Surgical thread comes in multiple varieties, including both monofilament and plied. If the thread (and surgical knots) do not have enough tensile strength, it risks rupturing, which is medically dangerous.
ATHLETICS
A lot of sports involve a copious amount of force. This means that the equiment involved needs to be able to put up with a lot of stress.
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For example, trampolinists depend on the tensile strength of the trampoline fabric. Likewise, aerialists require that their silks are strong enough to support their weight, and climbers require strong ropes so they don't fall. This means that when designing equipment, care must be placed into ensuring tensile strength.
ARCHITECHTURE
There are a lot of architechural applications of plying, too. Steel cables and ropes are frequently used for various applications.
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One of these is bridges -- particularly, suspension bridges. Given that they are supported by cables that undergo an extremely large amount of tensile stress, it is vital that their tensile strength is sufficient. This is especially important to ensure the safety of all the children that are inevitably jumping on them.
