Apply a function to many data frames

The following is an example of a question that has been asked several times in the past, but I have not seen a fully satisfactory answer. I would like to know if newer strategies have been developed, or if there is no convenient way to get to the desired result.

The typical question asks if a function can be applied to several data frames. An example is:

df1 <- data.frame(x = rep(3, 5), y = seq(1, 5, 1), ID = letters[1:5])

df2 <- data.frame(x = rep(5, 5), y = seq(2, 6, 1), ID = letters[6:10])

Above are the two (of perhaps a long list of) data frames, and what is desired is to add another column to each of the original dataframes which displays the average of that row. A typical answer is:

lapply(list(df1, df2), function(w) { w$Avg <- rowMeans(w[1:2]); w })

However, this does not change or add a column to the original data frames, but produces the following:

 [[1]]
   x y ID Avg
 1 3 1  a 2.0
 2 3 2  b 2.5
 3 3 3  c 3.0
 4 3 4  d 3.5
 5 3 5  e 4.0

 [[2]]
   x y ID Avg
 1 5 2  f 3.5
 2 5 3  g 4.0
 3 5 4  h 4.5
 4 5 5  i 5.0
 5 5 6  j 5.5

Question: Is there a procedure to apply a function to many data frames in a way that changes those dataframes directly?

I looked at many questions and answers, but they were basically the above strategy. Here is one example: Same function over multiple data frames in R