The book was first published in 1836, 186 years, and is still in publication and is still used by some guitar teachers. Not a bad run for a guitar tutor book. The review was written by Narayan Kumar who appears to be associated with this website and forum:
https://www.classicalguitarcorner.com . It costs money to join and I am not a member. I found the article searching for something else and thought it had a useful discussion about some aspects of Classical Guitar as well as being a review of the book. The download of the original book in PDF format was free from the review, that may not last forever.
This is a quote from the introduction to the article: "Carcassi’s Method for Classical Guitar was first published in 1836. It is still going strong through its various editions. For a good reason. It works. For a modern student who wants to learn the key concepts of classical guitar playing without spending too much time, the Carcassi method is ideal. The main method section is hardly 90 pages long. It is fast paced and deals with essentials only."
I am not a teacher and I suggest you read the article and make your own decision. Its easy enough to download the PDF file and print the book for free. Make sure you read it all the way through to the end and particularly the timescales which the author thinks is "without spending too much time".
This is the closing sentence, referring to the 25 Studies in the book : "As many a student has found out, these studies will keep them company over decades"
I am no expert on classical guitar and I am not all that interested in becoming an expert or "scholar" in the instrument. I just like to play my guitar. I did lessons for a year 30 years ago. Now I just read the music and play it.
If you really want to learn "Classical Guitar" and perform at concerts as a "Classical Guitarist" you should find the right teacher and do the study, part of the genre is knowing all the stuff, its not just playing a guitar. And even though this is several years of work, I think that you would enjoy the outcomes if you put in the work, but I never bothered with that level.
Teaching yourself from a book wont cut the mustard unless you are like me, a self indulgent musical instrument owner who never performs for anyone except themselves. But if you are old, and don't care much anymore, it could be a good starting point and may lead you to get the confidence to approach a serious Classical Guitar teacher for lessons or just help you be able to sit out and watch the sunset with a G&T and your guitar and some friends.
So read the article and make up your own mind if the method is for you.