Bearing in mind most pro bikes weigh more than 6.8kg, if there was no UCI weight limit, would they be lighter? Would show casing super light bikes be a dominant factor?

Flat courses - strength above weight. Not much would change. Many pro TT bikes weigh in near 8 kg!

Racing in the mountains: every gram counts. Every climber already makes sure his bike is no gram above 6800. Bikes would be extremely light. Especially if the finish is uphill, the top climbers would switch to ultralight climbing bikes. Mechanics would go all out for these to give their riders a competitive advantage, mounting only a single front ring, aluminium cassettes, no bar tape, Berk saddle/post combinations, etc.

However, this would all mean that riders could gain a competitive advantage through equipment, which is the number one thing the UCI is opposed to.

Ahh, except for hill climb time trials, most mountain courses, including those with mountain top finishes, include descending. Or are you suggesting that riders would switch bikes before the final climb (unless it's a long monster climb. it may be hard to make back the time lost in making the switch).

Switching was done by some before the 6.8kg rule came in. On a long climb and descent it could make sense despite the switch time, especially if you have a special descending bike that will be faster than a "standard" set up going downhill. Depends on the course.

You could easily get an all purpose bike down to about 5kg nowadays and I'm sure we'd see that, and even lower for some stages if there was no 6.8kg.

I'm no engineer first off, but I feel some of the better ways to these uber-light pro bikes should go now and maintain 6.8kg is now thinking through where they have the added weight. Simple things for instance, keeping the rolling resistance light so maintain light wheels for quick acceleration, and adding more weight to BB/center of the bike for added stability, and all the other ways a smart physic-oriented mechanic could come up with. Curious if this would make any difference.

My guess in the first year or two you would see some folks try bikes as low as 12lbs but IMO the fad would fade much like the fad of using very deep TT wheels for regular stages has come and gone. I doubt very much it would make any difference to the outcomes of the race. The tactic of switching bikes mid stage is not even clear. 30 to 60 seconds or possibly more time is lost in the switch alone. Ubbar light bikes also don't always descend that well at the highest speeds from my experience. Ubbar light bikes can be more susceptible to damage in the day to day abuse and ubbar light replacement parts cost more and can be difficult to get on short notice. They often need more tweaking to get them functioning properly. We also have the trend of powermeters/gps being added and who knows what other must have gizmos lurk in our future

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WW Velocipedist Gargantuan

Even a mountain stage isn't just about climbing, which is where light weight is a definate advantage. It's also about decending and often there's a fair bit of flatish riding as well which many would argue is better with a grounded heavier bike. Like rustychain I am not sure a change over is likely. It's not happening now despite the fact that bikes are overweight already. I am sure Wiggo's big Pina is at least 7.5kg.

The other thing reliability is high priority for a pro rider. The real lightweight stuff generally would struggle to survive a daily appetite of 190k of super hard riding.

Nope.
Wiggo is a notoriously fiendish WW at heart, check the details on his bikes. He brings that thing down to 6800g and not a gram more.

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Exp001

I highly doubt that
1st offender would be the frame
2nd would be the srm crank with the funny rings
3rd electronic drive train
4th large bars and long stem
Everything in his bike if notable for not being the lightest out remarkable light, like dura ace pedals among other accessories.

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For some of the mountaintop finishes in the pre-tour races he was seen running Enve rims laced to tune hubs. That's pretty WW to me, especially considering Sky are sponsored by Shimano.

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"Stay cool and try to survive" A. Klier to the other members of the Garmin classics squad the night before P-R.

Those wheels will still be upwards of 1200g if in the 50cm range.

Wiggo uses Speedplay Nano pedals. Also, the ENVE's in question was 1.25 rims on light hubs. More like a 1000g wheelset. So I don't think that bike was over 7 kg.

There's a fair chance that he has a lighter frame as well. The Pros often gets special frames with different layups. Tour tested some of Katushas Focus bikes, that were lighter than the shop frame. Likewise the danish "Cykelmagasinet" tested one of Saxo Banks SL4's build for Tour de France. The frame weighed over 1300grams!!! Needless to say, it was insanely stiff.

Wasn't the stock SL4 stiff enough? By the way I was always wondering what was the actual weight of Sagan's frame.

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Wilier Cento Uno
Colnago Master X-light
Wilier 18carati

The frame is a large and it is well known that he rides a stem on the longer side. Medium dogmas are about 1100-1200 grams and the fork should be around 350 grams cut and the seat post is 255 grams for the fuselage alone we are looking at 1800 grams + dura ace with osymetris rings which I am guessing come in at 800 grams, and then we add nanograms which are about 180 grams.
that is a total of 2760 grams for frame cranks and pedals. All of this are just my estimates but anyone has a similar configuration or knows the exact weight of Wiggins bike parts.one thing I could be sure his frame its not lighter than the production.
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The optimum weight of a pro bike is that which the rider prefers.

"Some people say that cucumbers taste better pickled." A weight weenie isn't going to be the optimum bike for a pure sprinter seeking a green jersey, and a stiff 8kg tank isn't going to be optimum for a small climber seeking polka dots.