I would suggest that the opinions on caste you're drawing from are highly incomplete, and driven by 19th century European scholarship. Hindu scriptures talk about varna, while the British formalized and elevated the unrelated and overlapping system of jati identity as the most important identity. When people think of caste today, they're thinking of jati, which are absent in the Hindu scriptures.

I would suggest that 19th Century Indologists conflated and confused two different types of descriptions of caste hierarchy in the Hindu canon. The Vedas, Upanishads, and Puranas are descriptivist, and rather matter of factly report a stratified society, where privilege and wealth was inherited largely within the family. This is no different than any other Iron Age society anywhere in the world.

There is also a prescriptivist strain within the canon, that suggests that the status quo is indeed optimal. The varna system described in the scriptures is not too dissimilar from the paradigmatic society of Plato's Republic: a hierarchy based on rule by Philosopher-Kings, and a division of society led by people best suited to it. Each person has innate qualities that endear them to one or the other major occupations, and society is most harmonious when people do the jobs best suited to them. The Vedas also suggest that these traits are largely familial, though this is not watertight. The scriptures are full of examples of people who transcend the varna of their family, and conversely there are no shortage of wicked brahmins and kshatriyas. Nor does the historic record show varna as a hindrance to social mobility in Ancient India. The Shunga dynasty was founded by a Brahmin, and the fabled Nanda dynasty by an erstwhile barber. The most famous of all ancient Indian dynasties, the Mauryan, was founded by a former slave, who belonged to a lineage of lowly peacock hunters. For contemporary Indians, these kings were not interlopers, but rather their military prowess proved that they were indeed Kshatriyas. The son of a Kshatriya King will likely be a king, but not always, nor must a king always be the son of a kshatriya. Usually, but not always. Indeed, the Bhagavata Gita, the definitive text for Hindus, states that all humans are born as shudras, or lowly, and it is their qualities and actions in life that elevate them. The British, however, took an obscure text, the Manusmriti, and used that as the authoritative matter on caste. The manusmriti is indeed vitriolic about keeping societal classes separate, but the class of smriti texts have no inherent authority.

As to the point that enlightenment is open only to brahmins, the considered opinion of the acharyas is that this is not true, and I can only think of a single textual example where this is a stated opinion of a (minority) Hindu school. A 16th century compendium of religious sects by a Gaudiya scholar stated that another school (madhva) held that enlightenment is open only to demigods and brahmins, and is understood more as a criticism of their beliefs. Every school after the bhakti movement of the 8th century has explicitly stated that worship and moksha is open to all, regardless of caste, or gender. I think the confusion arises from debates starting from the 8th century, if moksha is only possible for sanyasis, or renunciates. Sanyasis can be from any caste, or any gender. Some schools did indeed believe that renunciation is a necessary prerequisite to enlightenment, and is not possible for the lay public.