More can (and, in this case, really should imo) be said, but u/Tiako did a good write up here about the axial age that you might find interesting.

The other answers you've been given are good explanations of the Axial Age concept, but I'd like to add a different perspective. You've actually asked two separate, and in my opinion disconnected questions.

Why was this such an intellectual era?

VS

Is there any speculation on what caused the rise of so many notable thinkers at around this time period?

There are some arguments to be made that historical factors around 800 BCE to initiate a more philosophically complex period in Eurasian history. I think Graeber's arguments about coinage kind of fall apart with the inclusion of the Jewish prophets, but that's beside the point. His larger assertion that market forces and debt were involved is still true.

Obviously, there was philosophy before this. In the Iranian world, the Zoroastrian Avesta had been developing for about 500 years. In India, the roots of a lot of Hindu philosophy can be found in the Vedas going back to about 1400 BCE. Most famously, Egypt and Mesopotamia had flourishing legal, scientific, and religious thought back to 3000 BCE, but between a combination of poor documentation and the loss of documents over time it's impossible to really know how consistent and/or spontaneous individual developments were prior to c. 700 BCE. Between the Mediterranean and northern India, the early Iron Age is also something of a historical dark age in many fields that causes the appearance of a sudden rebirth of writing whether or not that is truly accurate.

However, the Axial Age really falls apart when you look for an end date. There's nothing particularly more intellectual about the period from 800-400 than there is for any other 400 year block in the same regions afterward. Ironically, the Chinese Warring States Period and the Mediterranean's Hellenistic Period are similar both in the politics of many warring factions and in their philosophical legacy. In both places, several new schools of philosophy developed and became quite popular in their own time, but with only a few retaining that popularity as new imperial powers favored resurgent forms of older systems (ie Platonism with Rome and Taoism with the Han).

In Judea, the Second Temple Period was a flowering of new ideas especially in the realm of supernatural, apocalyptic, and messianic beliefs. Some of these ideas filtered down in early Rabinnic Judaism in documents like the Talmud, but they were arguably much more influential in early Christianity. Obviously the ideas of apocalypse and a Messiah are foundational elements there.

In India, many new schools of Hindu thought developed during and after the Mauryan period as well, the political philosophy of the Arthashastra is obviously tied to the Maurya, but Yoga also developed under the Mauryans. There are several other Hindu schools that developed over the following centuries and are still followed in different ways today.

Moving into the first few centuries CE, it's not like intellectual development stopped. All of these philosophies that had been developing since 700 BCE still existed and still had their followers. Many fell in and out of use depending on the politics and social situations of later generations. Likewise, new schools of though have continued to develop over the centuries.