Plant proteins versus animal proteins.  An ongoing debate.  Multiple points of argument.  Addressing protein quality.  Animal based proteins are superior to plant proteins, with the exception of soy proteins.  Consider that 100 g of pea protein, 100g rice protein, and 100g whey protein are only equal in simple compositional analysis; however, they are not equivalent based on protein quality (be assessed by the Digestibility-Corrected Amino Acid Score (PDCAAS), or the Digestible Indispensable Amino Acid Score (DIAAS)).  Vegetarian diets combine plant proteins, such as those originating from grains and legumes, or grains and nuts, to meet healthy growth and sustenance (e.g. corn and beans; lentils and rice). Processing may improve properties of plant proteins.  Hydrolyzed rice proteins have improved solubility, digestibility, and bioavailability.  However, same advantages may be found in hydrolyzed animal proteins, e.g. hydrolyzed whey proteins have enhanced muscle building properties. Any advantage that a food may have regarding its content of unsaturated fatty acids may be compromised by the presence of oxygen, be it in the head space of the packaged product or exposure to air when opened, also may degrade during processing via dissolved oxygen in the aqueous or lipid phase.  Furthermore, any advantage that a food may have regarding its vitamin content may be compromised by exposure to air or the extent of heat processing.   There is a debate around using plant-based beverages as substitute to milk.  Most of these plant-based beverages are manufactured starting with a flour (e.g. oat flour, pea flour, almond flour) and using amylases to hydrolyze the starch. Simply said, these plant beverages are stabilized slurries of hydrolyzed flours; some have limited addition of vitamins and minerals.  However, those plant-based beverages provide an option to consumers that exhibit lactose-intolerance or milk protein intolerance or allergy.  Hence, a general broad statement that plant proteins are superior than animal proteins may not consider the multiple points that support the holistic value of a food. 

I think that the only suggestion for maintaing good health is not a plant-based diet but a diet without processed or supprocessed foods...

I think even the author of this paper would agree that its title is simplistic (although certainly likely to generate media interest).
Firstly, the answer depends on which animal products and plant-based alternatives we are discussing. If comparing a highly processed, high fat red meat with an unprocessed legume, then I would agree with the title. However, if comparing milk and oat milk, the nutritional and health benefits are clearly better from milk, and the environmental aspect dependent on choice of functional unit (10.3389/fnut.2022.957486). And in other cases (e.g. eggs, fish), functional alternatives are, in most parts of the world, not available.
Secondly, the quantification of healthiness is challenging. From a nutritional perspective, the animal and the alternative have quite different content and bioavailability (10.1071/AN21235). From a public health impact perspective, I would agree with the title in most cases, but not for example in vulnerable populations in LMICs, where low diversity plant-dominant diets are a driver of malnutrition.
Environmentally, it really depends upon your functional unit. Should we compare carbon, water, land use, or biodiversity? And per kg, per gram protein, per $? In most cases the author's assertion will be correct, but not in all (10.4060/cb8054en).
In general, it is better to compare diets rather than individual foods and understand that there will not be a simple X is better than Y answer. There will always be trade-offs.

Simply put, NO
Plant derived protein is less accessible fro theGI tract, being unsuited for people with digestive disfunctions. Plant aminoacids do not fully reproduce animal aminoacids, so defficiencies may arise. Moreover, relying on genetically modified and ultraprocessed soy as the main source of protein is unhealthy.

My take is that the answer to this question  is not best represented in a binary context. A purely plant based diet is not the healthiest option rather there should be a balanced with some animal based products. 
The problem arises due to the net result of animal farming practices that has resulted in significant damage to the environment. Whereas the mere encouragement of plant based agriculture has the simultaneously advantageous of trapping greenhouse gases and a plethora of positive climatic modulations.

In a perfect world both plant and animal foods would be healthy. The problem today in the US is that commercial interests are more powerful than health interests. In many neighborhoods, processed food is more widely available than fresh foods and it is less expensive. Our meat is produced by administering the animals with hormones and antibiotics because it provides a greater profit. Processed foods also produce great profit for the companies that produce them. Our government does not offer much protection to its citizens because it is also influenced by lobbyists. Fresh, home-cooked meals are an anomaly for many. We are in a health crisis in this country. 
 
 Eating a plant-based whole food diet, that is mostly organic, seems to be, quite frankly, safer for long-term health. Providing you supplement it with vitamin B-12. 

Plant-based foods are often considered healthier than meat because they  have low saturated fat and cholesterol with rich fibres, antioxidants and essential nutrients that support heart health and the digestive system. Diets rich in whole plant foods such as vegetables, legumes, fruits, and whole grains have been reported to lower the risks of chronic diseases such as diabetes, certain cancers and heart disorders. 

Plant based food products are healthier than meat. Because they are rich in vitamins, Fiber's, Anti-oxidants and other essential amino acids like cysteine, cystine and methionine that are link with lower cholesterol and lower risk to diabetes, heart attacked, obesity and certain cancer. but in case of meat provide complete protein, B12 and other essential nutrients. Ultimately, a balanced diet which including plant and animal based products are healthiest and most sustainable choice.