This, "experimental archaeology" as it is called, is of huge value. While it can be (and is) done in the absence of written records, it can be easier, more reliable, and with more useful results, when written records are available (just as archaeology can be a useful source of data for history, history can also be a useful source for archaeology).
Experimental archaeology goes back to the 19th century (if not earlier). For example:
includes experimental archaeology.
Despite its potential usefulness, experimental archaeology is somewhat of a fringe field. Partly, this results from the skills required to do it well - to study how to use technology/artifact "A" to do task "B" can require knowing how to do task "B" with other technologies, and this can restrict the number of people who are capable of doing this work well. Experimental archaeology can also be expensive in money, time, and labour - witness the trireme Olympias, which cost $700,000 (1989 US dollars) and took two years to build, and needs a crew of 200:
Coates, J. (1989). "The Trireme Sails Again". Scientific American, 260(4), 96-105. http://www.jstor.org/stable/24987219
Partly, the fringeness of the field results from poor quality work (including work by both professionals and amateurs), and misuse of the results.
The limitations of experimental archaeology need to be kept in mind, and they are not always kept in mind. Just because we find that technology/artifact A can be used for B, it doesn't mean that A was used for B. An experimental archaeologist might find that a spanner can be used to drive nails, but a spanner is not a nailing tool. If we fail to discover how to use A for B, it doesn't mean that A wasn't used for B. We might find that a replica linothorax made of layers of linen glued together works:
but it doesn't mean that the historical linothorax was made in this way. Solution to part of this problem is to do many more tests. But this brute-force approach runs into the time and money problem. One method is to use computational simulations rather than physical tests. I discussed this at the end of my reply to https://www.reddit.com/r/AskHistorians/comments/d8e5yf/what_is_computational_history_and_how_useful_are/ earlier today.
For an early history of experimental archaeology, see:
For some newer works covering the history of the field and presenting a modern overview, see:
Flores, Jodi Reeves, and Roeland Paardekooper (eds), Experiments Past: Histories of Experimental experiments Archaeology, Sidestone Press, 2014.
Millson, Dana C. E. Experimentation and Interpretation: The Use of Experimental Archaeology in the Study of the Past, Oxbow Books, 2010.