There are a few reasons that this is so slow:
First, the bit rate is likely on the order of 1-2kbit/s - it's bloody slow.
Second, RF is unreliable, particularly this kind - so the message gets sent a bunch of times in succession, often 5 to 20, and of course needs a checksum to know when it got through.
Third, libraries will often send a "training burst" at the start of each packet - a period of 50% duty cycle to get the AGC to adjust itself appropriately. This adds overhead.
Automatic Gain Correction (AGC) - this makes it possible for dirt cheap receivers and cluttered radio spectrum to produce decent results - it continuously monitors the strength of the signal (or noise) received at 433MHz, and adjusts the gain and threshold to get approximately 50% duty cycle output. This is why, when transmitter is off or on continuously, they output random noise - they crank the gain up until the noise gives a 50% duty cycle, and why these libraries that look strange and bizzare under the hood are needed - the receiver needs to be able to recognize the signal and pick it out against a background of continuous gibberish. This is also why a training burst and repetition are used (sometimes the transmitter will just repeat the message more times).
Also, with most RC toys, you've got functions like "right" "left" "forward" "back" etc, that run for as long as the button is held down. The transmitter transmits the appropriate pattern continuously. I'm not sure most RF toys use the same sort of 433MHz/315MHz OOK modulation scheme with AGC that the cheap 433MHz RF stuff uses - I know most of them are on different frequencies. 433MHz is typical for car door remotes, garage door openers, doorbells, etc
That sort of mode, continuously transmitting a single pattern, would indeed get a much faster response (you'd need your own library though, VW does things that aren't appropriate for this use case) with 433/315MHz OOK modules too - the continuous transmitting keeps the AGC locked on, and since you're not repeating each message plus training burst a ton of times, you check the buttons (assuming a RC-toy type use case) between each copy of the message.
Finally, don't use those awful green receivers - the green ones with that little thing with visible coil in the middle which seem to be the most common online and which I suspect you're using. Put them straight in the trash. Not only is their range lousy, I've seen them get into a state where the range falls off to a few inches (after unplugging and letting them sit a while, they work again - it's wacky). Get the RXB12 receivers on ebay (or RXB14) - they are under $2 shipped, get way the hell better range, and work on 3.3v with barely any loss of range (compared to almost complete loss of range with the shitty green ones) - they use a superheterodyne topology based on the SYN470 or SYN480 receiver, instead of the primitive superregenerative receiver in the green ones. Excellent performance - they beat the other typical cheap ebay receivers, even the $7 ones.
The green transmitters that usually come with them are fine though. There isn't much difference between the common OOK transmitters. Not even 2:1 in my testing, vs like 20:1 between RXB12 and the green receivers.