Why is everything based on likelihoods even though likelihoods are so small?

Suppose I generate some random numbers from a specific normal distribution in R:

set.seed(123)random_numbers <- rnorm(50, mean = 5, sd = 5)

These numbers look like this:

 [1]  2.1976218  3.8491126 12.7935416  5.3525420  5.6464387 13.5753249  7.3045810 -1.3253062     [9]  1.5657357  2.7716901 11.1204090  6.7990691  7.0038573  5.5534136  2.2207943 13.9345657    [17]  7.4892524 -4.8330858  8.5067795  2.6360430 -0.3391185  3.9101254 -0.1300222  1.3555439    [25]  1.8748037 -3.4334666  9.1889352  5.7668656 -0.6906847 11.2690746  7.1323211  3.5246426    [33]  9.4756283  9.3906674  9.1079054  8.4432013  7.7695883  4.6904414  3.4701867  3.0976450    [41]  1.5264651  3.9604136 -1.3269818 15.8447798 11.0398100 -0.6155429  2.9855758  2.6667232    [49]  8.8998256  4.5831547

Now, suppose I calculate the likelihood of these numbers under the correct normal distribution::

likelihood <- prod(dnorm(random_numbers, mean = 5, sd = 5))[1] 9.183016e-65

As we can see, even from the correct distribution, the likelihood is very, very small. Thus, it appears to be very unlikely in a certain sense that these numbers came from the very distribution they were generated from.

The only consolation is that the likelihood is even smaller when coming from some other distribution, e.g.

> likelihood <- prod(dnorm(random_numbers, mean = 6, sd = 6))> likelihood[1] 3.954015e-66

But this to me seems like a moot point: a turtle is faster than a snail, but both animals are slow. Even though the correct likelihood (i.e. 5,5) is bigger than the incorrect likelihood (i.e. 6,6), both are still so small!

So how come in statistics, everything is based on likelihoods (e.g. regression estimates, maximum likelihood estimation, etc) when the evaluated likelihood is always so small for even the correct distribution?