What Basavanna seeked to achieve was to create a casteless society, but what instead happened was that Lingayats just replaced Brahmins as the uppermost caste in North Karnataka.

Source: File:Castes and Tribes of Southern India, Volume 4.djvu - Wikisource, the free online library
The following is the ritual hierarchy of castes in North Karnataka. As you can see the Lingayats occupy the top most position followed by the Brahmins, Vaishyas and Jains. Another interesting observation is that the Rajputs and Marathas don’t enjoy the prestige they get in their home states in Karnataka. They are placed below the Vaishyas and the landed native agricultural castes.

Source: Traditn Econ Vill Ind Ils 74
The Lingayats also have an internal caste hierarchy with the Veerashaivas at the top. The Veerashaivas usually refers to the Jangams or priests. Nowadays it also includes the Banajigas (Traders) and the Panchamasalis (Landed farmers present in extreme North Karnataka and South Maharastra, they were previously Jains who took to Veerashaivism).
The following is the internal hierarchy among Lingayats.

The priests (Jangams) are the uppermost caste with the Hiremaths (the oldest lineage) at the top, they are followed by the other temple/worship associated castes like the florists and the Pujars. The Jangams were derived from the Brahmin (who took to Lingayatism), Banajiga and Panchamasali communities.
The Banajigas who are rich traders that finance the Lingayat mutts and who by the nature of their occupation are considered more ‘pure’ than the Panchamasalis that work the fields, come next. The Panchamasalis are placed above the Sadars (who are also landed farmers) because the latter allow widow remarriage and are later converts into Lingayatism.
You’ll notice that the prestige ranking of occupation presented in the first image does not correlate well with caste hierarchy within the Lingayats. The Banajigas or traders have a higher ritual status than the Farmer/Headman. This is because of the extremely ritualistic nature and the puritanical belief systems and practices among the Lingayats.

Well, imo it’s because the Veerashaivas have taken over Lingayatism. The Veerashaivas are the economically and socially powerful castes that once formed the warlords and rich traders of North Karnataka. They are called Veerashaivas because they followed the Shaiva order of Hinduism.
This is an excellent 3 minute video summarising the Lingayat and Veerashaiva history. Kindly watch it to understand how the Veerashaivas came to merge with Lingayatism.
The very basic tenets of Lingayatism and Veerashavism differ.

But the Veerashaivas control the direction and flow of the Lingayat movement even today. Majority of the Lingayat math heads and political leaders come from the Veerashaiva community. All of the Lingayat Chief Ministers have come from one of the following castes.

It is natural for powerful communities to try to retain their ritual status and power in society. Lingayats are also victims to this natural trait.