R needs it's own language because one of the most important factors in it's widespread use is the language itself. First, it is very similar to an older language that is one of the first widely used statistical packages. Second, the syntax is very easy to use at a simple level. For example, to read a csv file and compute a linear regression with betas, p-values, the works, all you have to do is:
# read a csv file with headers into ram
data <- read.csv(file='blah.csv', header=T)
# compute a linear model with dependent variable income, explanatory variables gender, education, and ethnicity, with automatic creation of (n-1) indicator variables as appropriate for categorical data
model <- lm(income ~ gender + education + ethnicity + age)
# if instead, I want to use a glm family of models, this is also trivial..
# note this is nonsensical statistically with respect to my data, but I just thought of this off my head, and it demonstrates how easy it is to do sophisticated things in R
model.glm <- glm(income ~ gender + education + ethnicity + age, family=binomial, link=cloglog)
That's it. So you can see why stats people love it -- it's easy to pick up and use to get productive work done. It's easy to show students. For what it's meant to do originally -- desktop statistics -- the language works quite well. It lacks as a programming language in many regards, don't get me wrong, but simplicity and ease of use, particularly in the beginning, are critical.
Also, the data frame is the single best data structure I've ever used for manipulating tabular data. Finally, the excellent repl makes working in R and exploratory analysis absolutely awesome.
It seems that way on the surface, but their are a lot of subtleties to R (lazy evaluation of function arguments, access to both static and dynamic scope) that would make implementation in another language difficult. R has many features that are not that desirable from a programming language stand point (and that do make optimisation difficult), but do make it a very expressive, flexible language for statistical computing.
Also, the data frame is the single best data structure I've ever used for manipulating tabular data. Finally, the excellent repl makes working in R and exploratory analysis absolutely awesome.