As far as I know, the romans never used semaphore. Maybe for practical reasons like not having telescopes, but maybe the idea just didn't occur to them. It would be pretty low hanging fruit for time travelers to introduce.

I think it was more due to not solving any problem. Same way despite Greeks inventing steam power, no one made engine from it cause there was no need. Too many slaves provided needed labor.

Runners, horses, ships moved communications fast enough. Even if you knew ceaser was coming to Rome, transport speed meant you couldnt do much with that. And yes we with hindsight cab cherry pick situations where it would help. But it was not worth cost to create, train and maintain such a system for hundreds if years for the fee.tumes it provided marginal benefit.

In other words most technology is synergistic. It really isn't awesome unless bunch other tech is at sufficient level to exploitmkit

But building and maintaining a semaphore system in a world that has slavery and where wood is cheap and plentiful (Caesar could build a bridge over the Rhine in 10 days, and that includes going out to find and chop down trees that are large enough) isn't that expensive.

The local HFT community would probably pay for a semaphore system. A lot of money could be made on knowing the outcome of events earlier than others.

On the other hand, "trees are plentiful" probably meant that sight lines were awful. Maybe, a semaphore only becomes feasible after one has cut down most of the trees.

Well sending a message that a remote province is being invaded, is useful. Especially if you can send that message days faster than runners can send messages. Its also very useful to coordinate ships.

The difference between steam engines is that steam engines were very difficult to build. Semaphore is very simple and a trial system wouldn't be expensive to set up.

The Romans did use crude fire signals, so I think that proves that they would find it useful.