Why do physicists think that the electron is an elementary particle?

Believe you me, people have devoted a lot of time to coming up with composite models of the electron, without much to show for it. For example, see the preon.

High energy scattering experiments have shown that the charge radius of the electron is very small, and yet the rest mass of the electron is also very small. It's difficult (though not impossible) to achieve both in a composite model.

Why do physicists think that the electron is an elementary particle?

Because:

1) The standard model considers the leptons elementary particles. As it describes very successfully most of the data gathered by particle physics studies there is no reason to question the hypothesis of elementary leptons.

2)experiments testing for compositness of leptons give only lower limits for the scale of the appearance of compositeness. See for example this recent publication from LHC data for electrons and muons.

The exclusion region in the compositness scale Lamda and excited lepton mass M theparameter space is extended beyond previously established limits. For L = M , excited lepton masses are excluded below 1070 GeV/c2 for e^* and 1090 GeV/c2 for mu^* at the 95% confidence level.

Compositness is completely unpopular with theorists but a number of experimentalists keep on testing for it when new data is available, which is as it should be.