You can't actually compare apples to apples immigrants to Europe and immigrants to the United States because the way immigration is conceptualized into legal systems are quite different. For one, the US, in spite of what the president attempts to proclaim, absolutely has a jus soli system of granting citizenship in addition to a partial jus sanguinis system that makes the determination complicated when citizenship is passed paternally and hinges on the year of birth and legitimization/recognition by the father for a variable number of years. This means that not even every person born outside of the US and entered the country later in life is necessarily an immigrant, and also conceptually there's no such thing as "second generation immigrant", since if they are born outside of the country and do not have citizenship when entering the country with intention to stay, they are immigrants. Otherwise, they are not immigrants. While the determination of whether someone is a citizen or not is actually a potentially complicated process that requires a court to adjudicate, it's only really relevant as a defense to orders of removal in the domestic context, as otherwise it's a consular processing matter that is resolved before the person enters the country. Although how one's actual status may be determined in a variety of circumstances and ways, it results in what's effectively binary - you are an immigrant, or you are not. Contrary to popular usage, "illegal" or "undocumented" is not a descriptor that has a set legal meaning and some are in illegal status for very short periods of time due to bureaucratic inefficiencies, and others are effectively relegated to second class citizenship with literally no chance of adjusting their status, period. While these are meaningful distinctions to make when talking about the issue, when it comes to calculating economic impact, because entitlements are broadly speaking not available to those who do not have legal permanent residency at the very least, the binary, thanks to the legal fiction of 'status', creates a bright line that splits bot along "legal" and "illegal" but "immigrant" and "non-immigrant" in reality.

While thanks to legally enforced discrimination based on the distinct American construction of race and ethnicity there are economic advantages and disadvantages that on the whole affects those considered by the state to be part of said minority group, it's not discrimination that results in immigrants across the board being economically disadvantaged. The immigration policies of the country have in fact so favored educated, white collar migration that there's literally no viable legal way for unskilled or lower-skilled workers to migrate at all, and this has been true legally since the mid 1960s and enforced fully since the early 80s. In absolute numerical terms, the most disadvantaged groups in the country are actually, broadly speaking, the offspring of persons trafficked over via the Atlantic slave trade and those whose ancestors entered when the country officially had open borders (true for all until 1882, and to most Europeans until 1924). I understand that the policy does not resemble the policy of any European country today and so may not be intuitive to those who don't have in depth domain knowledge on the background and legal landscape, which includes most Americans. I know this because I have an Area Studies degree and have practiced immigration law and so while I can't tell you how to obtain a divorce, form a trust, or legally dodge taxes, this happens to be a niche that I worked full time in, and Cato's studies follow how the administrative agencies in charge of immigration and the demographics of migration in this country have decided to demarcate the population. Some of the legal language is copied verbatim from the 1880s but since congress refuses to implement meaningful fixes beyond addressing nonexistent problems since the Clinton administration, one has to work with the data that exists, not the data that we wish existed.

It also is quite obvious to anyone who actually knows how the system works. Everyone is required to pay income taxes federally and many on the state level as well, but immigrants do not receive most entitlements. Even those present legally are not entitled to the full slate of public entitlements that form the bulk of the deficit that grows year after year. Without social security numbers, they can nevertheless obtain taxpayer IDs (ITIN) that follow the same format, but do not generally have withholdings and do not benefit from tax credits except those that benefit their US citizen children, which of course are meant for, and really only sufficient, for their children. Most immigration benefits are funded by the applicants and are not cheap and with no guarantee that they will receive the benefits. It's accurate to say that many not only are many immigrants stuck in an eternal situation of taxation without representation, but in fact they are paying to fund their own persecution, coerced by the state of course. The ponzi-like structure of social security is kept afloat in part thanks to immigrants paying into it but unable to benefit from it later. While most who talk about taxation as theft are really speaking metaphorically, for immigrants who receive no benefits but are forced to pay for everyone else's and have no say in the matter at all, it's far more literal, and kafkaesque.

Your proposed methodology may very well be valid for Europe, but in America it would be essentially impossible to conduct a study on the entire population to begin with, and studies that uses heuristics show the opposite than what your assumptions indicate. Cato is a policy think tank and while its publications may be of interest to the general public, the focus is on promoting policies in the classical liberal tradition and meant for members of congress, federal and state government decision makers, and others who can influence policy. It's not their job to explain immigration law to people on twitter, and frankly, those people don't care about what the law actually is anyway. They ask questions clearly without understanding the context that the paper actually explains, and nobody is obligated to chew the meal they cooked for you as well, you know.