The “default” LTspice transistor is idealized. Real ones aren’t that good :)
Transistors are *called* “switches” but they are not literal switches like a toggle switch is – they are not mechanical contacts.
Perhaps inadvertently, you have set up the transistor as a common-base switch, and that has a chance of working acceptably – you just need some load, the output can’t float.
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The component values do depend on the parameters of the transistor, and have to be adjusted in practice. It's not the best way to implement a switch, but it certainly works well enough to be useful for something.
The general idea for common-base switches is having ample amplitude of base drive. Ideally, the base drive would be a current source.
Below are the input, output and control waveforms of the circuit above. The control waveform's amplitude is scaled down 50% to make it fit better in the plot.
[![Plot of I/O waveforms, and the control waveform][1]][1]
The non-linear distortion is about 0.5%. The input, output and distortion residue waveforms are plotted below.
[![Plot of the I/O waveforms and the distortion residue while the switch is on][2]][2]
A more dependable way to implement a bipolar switch would be to convert the input signal to a current, then switch the current between two resistors, and take the output from one resistor only.
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The switching action is clean:
[![The output voltage waveform as the switch switches][3]][3]
The distortion residuals are <0.1%:
[![The waveform of distortion residuals][4]][4]
[1]: https://i.sstatic.net/3b8An.png
[2]: https://i.sstatic.net/kFEAA.png
[3]: https://i.sstatic.net/mZMeu.png
[4]: https://i.sstatic.net/aUPId.png