As someone who cycles every day, has done so for the last 20 years and rides a variety of different bikes (I’ve got 6), I can probably help on this one...
Basically people with this problem are often trying to sit on the wrong part of their body and/or have the wrong length saddle for their riding position.
I’ll start with the first problem of sitting on the wrong part.
What people often try to do is treat a saddle like a chair and attempt to sit on the fleshy parts of their bum — on the glutes (arse muscles). Instead what you want to do is sit on your “sit bones”. The sit bones are part of your pelvis and can be found on either side of your balls or vulva (depending on your biological sex, naturally). It can take a little time to get used to having pressure on your sit bones. Using padded cycling shorts can help with making the transition to regular cycling, and can be necessary if you do more than an hour per day in the saddle even for experienced riders. The temptation is often to get a bigger, softer saddle but this will have the effect of putting pressure on your squishy bits, so even if it feels more comfy when you first sit on it, within 5 minutes you’ll be hurting. You want a saddle that is only slightly wider than your sit bones.
The 2nd part of the equation is saddle length. The long and short of it is that you need a shorter saddle for more upright bikes and a longer one for bikes with a lower front stack. This is because if you are more upright your kegs would rub on a longer saddle. Your local bike shop can tell you what saddle length is appropriate.
There is one more thing to think about and this applies especially to women, and that’s the gutter in the middle of the saddle. Many women find a deep gutter can help take pressure off their vulva and keep the weight on the sit bones.
In conclusion, no their isn’t a giant conspiracy by the cycling industry and local bike shops to hurt you. Instead you just need to update your technique so that you are on your sit bones instead of the fleshy bits. A smaller, harder saddle is going to be infinitely more comfortable than a big squishy one.
Trust your local bike shop, and if you are having difficulty adjusting get some padded cycling shorts.
Good saddles I have experience of using include Brooks (various leather saddles depending on the bike) Sella Italia Turbo (I use this on my single speed) and Fiz:ik Areone (SP OK?). None of these are cheap but cheaper, good saddles are numerous.
Trust your local bike shop and lean in to it. It might take a few weeks to adjust, but you’ll get there.
+1 for this. Also, in my experience the SQLab saddle system with different widths depending on anatomy and posture on the bike makes a lot of difference. I'm running SQLab saddles on 75% of my bikes now - the commuter/beater won't get a fancy seat for the short distances I ride it on.
Similar models ought to exist worldwide. Though in general, following the advice some of the other posters have given is more effective.
Most people can use normal saddles. I would recommend getting one suitable for your plumbing down there though (i.e., unisex is convenient, but a good saddle tends to be suitable for either penises or vulva's, not both).
There's models without the front bulge (aimed at people wearing dresses so it doesn't show a bulge coming from between their legs). Were the angles of those seats adjusted accordingly? Might work better for you if they're angled downwards. The majority of the weight should be on the back side, the middle part is more to prevent rotating motions [citation needed])
I assume it’s not really possible to make a saddle with a radically different shape that still supports the rider and allows their legs to pedal the bike.
For what it’s worth after some time in the saddle your body will get used to it and it’ll be less uncomfortable. Even now, after decades of cycling, it takes a while to get comfortable again after a prolonged period off the bike.
More usefully, upright bike saddle fit is largely about the spacing of your sit bones. There's tutorials online on how to measure that, and some saddles tell you what spacing they're designed for. The alternative is to go to a proper bike shop and try a variety of saddles to find on you like. But it's tedious, because seat height, handlebar height, handlebar distance, seat to pedal horizontal distance and fore-aft tilt all affect that too.
If it really bothers you pay for a "bike fit", there are people who do this for a living and can make a huge difference to how you feel on the bike.
Why the hell is the default shape a gooch destroyer? I'd rather a round wooden bar stool seat than that.
I literally can't find anything except that design online either.