Photographers have been using cameras for over 100 years without live view.
Thought-Provoking..... Has me wondering that the Single-Lens-Reflex mechanism is sort of an rather overly elaborate automation of the old 'plate' cameras with a ground-glass view-screen replaced manually by a photographic plate, and the fact that the original 118yr old Box-Brownie had NO view-Finder what-so-ever, and many film-cameras, right up until the end, had no through-taking-lens view-finder, if any at all! My 1950's Ziess Ikonta just has a wire-frame composition guide, and I have had little key-chain / Christmas cracker 110's that didn't have much different!
Slight tangent to the topic, though; the 'niggles' with Single-Lens-Reflex mechanism's are nothing new, and the 'mirror-slap' REALLY, isn't a big one! ISTR it was something that Hassablad made a big shout about many moons ago, because it was something they claimed to have 'solved' when it was noted 35mm SLR's of the chunkier construction might suffer it, and folk suggested would be an enormous problem on a camera with a 4.5cm sq mirror, rather than a 2.5cm Sq one. On a modern DSLR with a mirror half that size, it should be even more minor issue than it was on a 35mm SLR of years passed.... where it wasn't, really!
It only really effected things if the camera was rigidly mounted on a tripod, and the shutter released on a cable. Self-Timer mechanisms were often recommended for such situations, as they usually tripped the mirror before the shutter delay, hence the lag between the mirror moving and shutter opening gave time for any vibration to dissipate.
Over-all, the SLR mechanism is a complete-camel of design..... the only 'real' problems it solved, was that of parallax error, the small shift in angle of view between separate taking and view-finder lenses... which was only of much issue at very short subject ranges, and many view-finder cameras tackled with the expedience of 'parallax-correction' marks or frames in the view-finder. Other was that inconvenience of having to change view-finder, or view-finder frame, with the lens on an interchangeable lens camera, and in the case of Twin-Lens-Reflex cameras the need to make paired and hence expensive and bulky lens-sets, to swap, and lugg about.
In many ways the SLR mechanism, made MORE problems than it solved! To make room for a mirror and pentaprism between the taking lens and the focal-plane, begged a 'retro-focus' lens.. ie one that compensated for the fact that the mirror box pushed the lens mount, probably 25mm or more ahead of the focal-plane, so shorter focal-length lenses had to be mounted further from the focal-plane than their focal length, and hence introduced 'deliberate' optical errors in compensation and multiplied them in manufacture. This was something that made range-finder cameras popular with more discerning snappers for many many decades over more bulky and convoluted SLR's. The bulk of the pentaprism, the reliability of the mechanics, all added to the problems they made for the little they solved.
It's interesting now, in the digital era, to hear a lot of the Film-Era knockers arguments against SLR cameras being re-hashed and re-interpreted, often with significant repetition-distortion by the exponents of 'mirror-less' digital cameras, as cause for their supposed superiority!!!! This suggestion of 'mirror-slap' sounding eminently like one!
As has been said; its pretty much a non-issue, and in the balance of competing compromises, a pretty small one! The SLR system is flawed, no doubt about that, but on the whole, the advantages, for more people, in more situations, either made no odds or outweighed the short-comings; hence the poplularity of the SLR for the best part of the film-era and into the digital.
For me, the advantages of a wider range of available lenses, more widely available and more economically available, for the incumbent DSLR's, is certainly one of the top reasons for picking one. The advantage of a pure optical view-finder, not draining battery power, not using a view-screen to be ruined by 'glare', the demand I hold the camera 'properly' not at arms length, and so more positively, are all 'advantages' of a DSLR I appreciate, for all the minor quibbles and potential problems to ultimate IQ that really pale in comparison to my basic ability! And THOSE were the reasons I bought a DSLR... with a convoluted flappy-mirror periscope mechanism, making it more complicated and more expensive than mirror-less alternatives.... and I see little reason to habitually ignore that I actually 'paid' for that minor inconvenience to look at everything on the relatively low resolution LCD screen on the back, at arms length, rather than ruddy use the camel I paid for! It's like buying a camel to cross the desert, then walking because a horse is faster?!?!?
So.... have you ever actually suffered 'Mirror-Slap'?
If not, it's a bit like keeping an Elephant in your loft to stop the tigers getting in your garden!