Why did post-Roman rulers abandon tax-paid army?

"abandoned Roman tax-payed army in favor of medieval feudal one, which was far worse."

Paying an army with tax money does not confer inherently superior quality. While one could argue European feudal armies were inferior to the Roman legions, this had very little to do with taxation and much more to do with the fact that the Romans had a large, professional, standing army.

The prime factor here is the diminished state resources available to most European rulers after the fall of Rome, which necessitated the reliance on feudal levies in the first place. Therefore,

"It looks as if it would give them a great advantage."

No, it doesn't, and it wouldn't.

"but why they did not use both or revive the former a century or two later?"

Actually, they did, just not necessary right away.

Over the preceding three hundred years war had become the preserve of a body of professionals, knights for whom it was a major source of income. This state of affairs had come about gradually and, in large part, as a response to the equally slow erosion of feudal military obligation. Of the eighty-seven knights present at Caerlaverock in 1300, twenty-three were paid for their service and the rest were either members of the royal household or men responding to the traditional feudal summons.

_{James, Lawrence. Warrior Race: A History of the British at War. Hachette UK, 2010.}

The main barrier was economics. When the Roman Empire fell, the economy of Western Europe was in shambles. The continental trade that had once flourished was replaced by small, largely (though not completely) self-sufficient manors. Economic weakness, compounded by an inadequate monetary supply meant it was easier to levy taxes in kind or in the form of services, rather than money.

Nonetheless, as the money economy of Europe recovered, mercenaries became more active in the latter Middle Ages. Liege lords hired them to complement feudal levies, and vassals hired them to fulfil military obligations. In some systems, mechanisms like scutage was developed to allow a vassal to opt out of military service by paying a fee, which the king then used to to hire substitutes.

The consequent reduction of the number of feudal troops available was largely offset by a parallel increase in the employment of stipendiaries and mercenaries . . . [M]any knights themselves, though still under feudal obligation, were also paid by the end of the 13th century,

_{Heath, Ian. Armies of Feudal Europe 1066-1300. Wargames Research Group, 2016.}

In essence, scutage was a tax; and it was regularly used to pay for an army.

"Once someone with a private army conquered a piece of land . . . it is strange to abandon the army completely"

The flaw in logic here is that those "private" armies were not paid in the first place, and especially not paid by taxes. They were personal retinues who served their leader due to personal obligations. Furthermore, these originated mainly from the Germanic tribes that overran the Roman Empire, so it would have been rather more strange for them to suddenly be paid like a Roman standing army.

There's also the glaring problem of having the money to actually pay for an army. As we saw above, even knights were paid to serve longer than obligation demanded; the challenge was having the money to pay with. Up till the end of the Middle Ages, most states only hired armies when they need to.

A traditional agricultural economy was usually not rich enough to pay for a permanent army staffed with large numbers of men well equipped with expensive horses, armor, and weapons. The net result was that rulers relied on short-term armies instead.

_{Janin, Hunt, and Ursula Carlson. Mercenaries in Medieval and Renaissance Europe. McFarland, 2013.}

No medieval state in western Europe could compete with Rome's financial resources or degree of centralised control; hence none of them

"from the evolutional point of view, the states without tax-paid army should not survive natural selection."

Perhaps, but evolution doesn't work off a couple of years. Eventually all the major feudal states of Europe that survived did adopt professional standing armies paid out of general taxation.

Moreover, evolution is all about the survival of the fittest in a given environment. If the "tax paid army" was truly so superior, the Roman Empire wouldn't have fallen. In reality, maintaining such an army was a massive economic burden, which was simply not realistic in most of Europe throughout the Middle Ages.