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I've been watching triathlon videos lately and I couldn't help but notice that, with the exception of Ironman Competitions, only road bikes and not time trial bikes are being used. Is there any reason for that?

The OP linked 4 videos, the first 2 videos were long-course Ironman races, where time trial (TT) bikes were used, while the latter 2 videos were of short-course draft legal races where road bikes were used. In the latter two videos the competitors were either pros or elite amateurs. These individuals typically have multiple bikes and would be using a TT bike if it was the right tool.

Originally, all triathlons used to have a no-drafting policy, which made optimizing your personal aerodynamics critical. Hence the rise of TT bikes in the early history of triathlons.

Relatively recently drafting has been made legal in many short track triathlons, making TT bikes both dangerous and not suitable for the format. When you have drafting you essentially have a road race, which a road bike is the right tool. Quick handling is key as you need to be able to maneuver and keep your front wheel within 2-6 inches of the bike you are drafting in order to get the full draft effect. You also need to be able to accelerate, brake, and change direction quickly to close gaps and respond to group dynamics. Groups can at times move incredibly fast, 65 kph on the flat is not uncommon for pros or elites.

In contrast, Ironman events still have no-drafting rules in place making TT bikes the right tool as its about individual riders against the wind and not responses to group dynamics.

NOTE: the answer is intended to address the races explicitly highlighted by the OP, not all world wide triathlon events, nor the large array of amateur races where participants may be balancing a number of considerations (e.g., cost).

Triathlon and time trial bikes are quite expensive and not wonderful to ride on open courses, hills, and in groups (in other words, general cycling).

So, if you're not so serious about triathlons that you're willing to spend several thousand dollars on a bike that will see relatively little use, you'll likely be content with your existing road bike whose handling and fit works well with your body and riding style.

In addition to Paul H's answer, there are several different triathlon distances from sprint to full iron man. In shorter races with hilly bike courses, or where there are many tight turns a regular road bike may be preferable.

Another lesser point is money - sport costs, and a triathlon is essentially three distinct sports in one.

The bike is an expensive item, and so making use of what you have is a perfectly good solution. For some competitors, that will also be their commuter come Monday morning.

I've even seen Mountain Bikes used in a triathlon, with road tyres and locked out
suspension.

My own observations do not agree with yours. In the Gulf Coast 70.3 this year there were a fair number of people on road bikes and even some on hybrids. There was one lady with a basket on her bike.

This past weekend, and many event like it, I attended an event where a they had a Sprint that had and Olympic distance at the same time through MultiRace. As usual there were many high end triathlon bicycles. Despite it being a no draft race, a road bike might be more suitable as the roads are really rough. It makes it difficult and possibly dangerous to remain in aero the whole time.

If you go to just about any event you will see a full spectrum of bicycles. Many, for cost reasons do like I did and have a road bike with clip on aerobars. Its very cost effective. Finding a used road bike is far easier then finding a used tri bike.