Why emphasise the EBT when anyone who has achieved Arhathood can teach from direct experience?

As well as the certain authenticity of the EBT -- how these close to his words -- and are his teachings -- you might wonder if an arahant and a -- dead -- Buddha, might have different audiences: different receptions within the same fundamental truths.

The Buddha and his immediate followers whom he declares has seen the unborn are sure Arahant, but how is one to assert a few century-old teachers as Arahant? I think that is why the written / oral transmission directly from the Buddha time is very important.

That doesn't mean that the living teacher is to be distrusted, teachers like Ajahn Chah are a living Dharma, but its's said that "The blessed buddhas are like never-setting suns intent on making the host of lotuses that are the disciples’ minds bloom with the extensive sunbeams that are their great compassion, methods and awareness" so their teaching should be seen a checkrein.

To add to OyaMist's good answer.

In the sutta below, we see that even one arahant (with no psychic powers) is unable to recognize another arahant.

Ven. Sariputta, the arahant and excellent teacher, could not recognize that Ven. Bhaddiya is an arahant, and tried to teach him. The Buddha saw this and was amused, because the Buddha himself is able to recognize who is an arahant and who isn't.

If one arahant cannot recognize another, then what hope is there for the unenlightened folk to try to do the same?

From Udana 7.2:

Then at that time venerable Sāriputta, thinking that venerable Bhaddiya the dwarf was still a trainee, was instructing, rousing, enthusing, and cheering him in abundant and countless ways with a Dhamma talk. The Gracious One saw venerable Sāriputta, who was thinking that venerable Bhaddiya the dwarf was still a trainee, instructing, rousing, enthusing, and cheering him in abundant and countless ways with a Dhamma talk.

Then the Gracious One, having understood the significance of it, on that occasion uttered this exalted utterance:

“He has cut off the cycle, gone to the desireless,
Dried up, the stream no longer flows,
Cut off, the cycle no longer rolls on,
Just this is the end of suffering.”

On the other hand, the Buddha left us his teachings (Dhamma) and told us to use this as our refuge, with no other refuge (apart from our own self-effort, of course).

From DN 16:

"Therefore, Ananda, be islands unto yourselves, refuges unto yourselves, seeking no external refuge; with the Dhamma as your island, the Dhamma as your refuge, seeking no other refuge.

So, would you rely on an uncertain arahant who you cannot verify, or the original teachings of the Buddha in the EBTs?

The Buddha's Dhamma is:

• Svakkhato: well taught and complete
• Akaliko: transcends time

Since this was not taught targeting a particular audience in a particular era and also since it is complete it is relevant today as well.

Without psychic powers, it's actually quite difficult to determine who is an arahant. Fortunately, the Buddha gave some guidelines in MN47 about how to assess a potential teacher:

MN47:4.1: “Mendicants, a mendicant who is an inquirer, unable to comprehend another’s mind, should scrutinize the Realized One for two things—things that can be seen and heard:

MN47:4.2: ‘Can anything corrupt be seen or heard in the Realized One or not?’ etc...

However, it's much easier to verify the validity of the Early Buddhist Texts (EBTs). Many scholars have compared these ancient scriptures as they were translated and written down in many different countries. The EBTs are remarkably consistent in doctrine. Having faith in the EBTs doesn't require psychic powers.

This principle of faith based on inquiry and evidence is fundamental in Buddhism:

MN47:16.1: When someone’s faith is settled, rooted, and planted in the Realized One in this manner, with these words and phrases, it’s said to be grounded faith that’s based on evidence.

Arahants do teach. Sariputta taught, as did Moggallāna. They had different styles. Sariputta was more into textual analysis and Moggallāna more into psychic powers. And both of their teachings were rooted in the Buddha's own teachings. However, without a Buddha to verify their arahantship, we need to rely on the methods of MN47 to establish a trust in contemporary teachers.

Lastly, the EBTs are continuously translated into contemporary languages and are therefore just as relevant today as 2500 years ago. Samsara goes on as it does while the wisdom in the EBTs remains directly relevant to this day and beyond.