A lot of instruments from the analog era were supposed to sound like other "real" instruments, and were as good as technology allowed then, which is not very. But over time, some have become popular in their own right.
Electric pianos were indeed supposed to sound like acoustic pianos (although some manufacturers saw the potential of adding features like tremolo). Hammond tonewheel organs were supposed to sound like pipe organs (and were marketed as a more convenient option for churches). The Mellotron was supposed to sound like a real choir or string section. The Roland TB-303 (which later became the sound of acid house) was supposed to sound like a bass guitar. The TR-808 and TR-909 (which later became the sound of hip hop and techno respectively) were supposed to sound like a real drummer. String synths such as the Solina String Ensemble were supposed to sound like a real string section.
None of these sounds very convincing compared to the real thing, or to more recent sample-based or modelling-based digital technology. But, as you say, they were cheaper, easier to record, easier to amplify, easier to carry around, and didn't require much tuning; so they were extensively used in popular music of the time, and are now considered "classic" sounds.
Hohner advertisement from 1982, highlighting portability and affordability and promising the sound and feel of a true piano: