Thanks for the contributions from jeffreyn, soccertese, tupelo3, TexasTom.

(L=levodopa, C=carbidopa, E=entacapone. In what follows below L means L and not L/C.)

So, the question is: Why is there no L/E medication available? And to clarify once more, that's levodopa and entacapone, but without carbidopa.

A literature search is made difficult because "levodopa" is often used to mean "levodopa/carbidopa". However, I did find a few references to unambiguous L and L/E.

Ahlskog writes [1]: "entacapone in the absence of carbidopa/levodopa has no anti-parkinsonian effect".

I see it differently however: L/E is likely to be slightly more therapeutic than L, but it is overshadowed by L/C which is better. L/C/E is better still.

The method of working of both C, a DDC inhibitor, and E, a COMT inhibitor, is to prolong the peripheral life of the L that they are taken with. So, we are interested in the metabolism of L: the metabolic pathways, their relative power, their metabolites. The metabolic pathways of L are [2][3]:

DDC, 70%, Dopamine
COMT, 10%, 3-O-Methyldopa
TAT, ?, 3,4-Dihydroxphenylpyruvic acid
Tyrosinase, ?, Dopa quinone
PST, ?, Conjugation products

So, the effect of DDC is much stronger than COMT. Moreover, as others have mentioned DDC inhibitors reduce the amount of peripheral dopamine, which is good because peripheral dopamine causes nausea.

References:

[1] "The New Parkinson's Disease Treatment Book"
p142,
Ahlskog J., 2015

[2] Benserazide - ScienceDirect Topics

[3] "Encyclopedia of Movement Disorders, Vol 1"
ed. Kompoliti K. and Metman L.
2010
isbn:1237415X - Google Search

John