Mail was relatively speaking cheap to make. This is because, at least before the Black Death in high medieval europe, labour was abundant and so the the primary factor of cost for armour and other items was material rather than labour/time. Labour dynamics did differ in the early medieval period, but what mainly lacked there was technology and an industry to support the making of plate armour limiting the choices of armour that could be made at all.

To make plate armour one has to work from large pieces of relatively homogenous iron and/or steel which is not something that is all too easy to acquire without the proper technology. What made this possible on a large scale was the introduction of the blast furnace. For a good source on this I wholeheartedly recommend Alan Williams The Knight and the Blast Furnace which goes very in-depth on the development of metallurgy and armourmaking in medieval europe.

Something like a helmet or greaves requires less iron to make than a late medieval cuirass, which is why these pieces were used earlier than late medieval plate armour was. However not all helmets were made of one piece either. In the early medieval period the majority of surviving helmets we have, such as the finds from Valsgärde or Sutton Hoo we can see that these are constructed with multiple pieces that have been riveted or otherwise joined together. The helmet found at the tail end of the early medieval period in Ghjermundbu also shares this segmented construction.

In the 11th century this trend has changed. We have several finds of conical helmets, many of them eastern European though not all, from the 11th and 12th centuries that have the skulls forged entirely in one piece.

In the 13th century however we see the appearance of the Great Helm. While the surviving examples all date to the late 13th century or later (examples would be the ones found in Dargen Pommern, or Bolzano) we see earlier forms of these depicted in the earlier decades of the century. What is important about these helmets though is that they're not formed out of one piece like the previously mentioned conical helmets. Presumably this has to do with their size, which is meant to accomodate a lesser helmet underneath it known as a cervelliere or 'secret helmet'. This is consistent with the observations done by Williams, which notes that the ability to create large pieces of iron homogenous enough for armourmaking was a development which happened later. So even if the technology to make smaller helmets out of one piece of iron was present, this could not yet be applied to larger helmets.

However, this does not mean that there were no forms of plate defences for the torso in high medieval europe. Before I go into that it should be noted that the end of the High Medieval period depends on location. While it's generally considered to have ended around the year 1300 in most of western Europe, the commonly given date in Nordic history is around 1350.

The earliest mention of a plate torso defence I am personally aware of is from Guillaume le Breton's Philippidos, dated to the early 13th century. In book 3 there is a poem describing a duel between the future King Richard 1 of England and Guillaume des Barres (or William de Barres). In it a worked iron plate worn beneath the mail hauberk is mentioned. The nature of this iron plate is not described. However to our fortune this is not the only source to mention such a plate. In the Norwegian Konungs Skuggsja, ca 1250, a similar plate is mentioned as being worn underneath the hauberk of the rider. This time we're given the dimensions as it's mentioned to reach from the nipples to the breech belt. Unfortunately neither of these sources tells us how the plate was worn and suspended.

The mid-13th century is also where a different way of wearing these plates appears and becomes gradually commonly listed in inventories. Instead of being worn under the hauberk we instead have a construction where they're riveted to fabric, sometimes to a surcoat, and worn over the hauberk or standalone. These are commonly referred to as 'pairs of plates' or just 'plates'. The earliest known visual representation of this is from a St Maurice statue dating to the mid-13th century held in the Magdeburg Cathedral. In it we can see the rivets of several smaller plates on the surcoat worn above a hauberk. This is an interesting contrast to the one-piece breastplates mentioned above, however for some reason this seems to become the dominant way of wearing plates in the 13th and early 14th centuries.

By the late 13th century this type of armour had become common enough that one could expect regular soldiers to wear it as well. A letter from Edward 1 in 1297 orders the gate watch of london to show up in three possible combinations; aketon and gambeson, aketon and corset (likely mail) or aketon and plates.

So to summarize; mail was popular because it was cheap and easy to make, even if time consuming it doesn't require advanced metalworking technology. Smaller plates of iron such as greaves or helmets show up first since they need less material to be forged, and gradually as metallurgy improves so does the coverage of plate armour. With the introduction of the blast furnace one can extract larger pieces of iron/steel which is what allows for the plate armour of late medieval europe to appear.

Edit: Some amendments to the original as has been mentioned in the comments have been made to make the claims more accurate.