no
a pedal point can be on any note or chord, in any voice
that said in tonal music a pedal other than tonic or dominant is quite rare.
- the supertonic (2nd scale degree) only really appears as a fifth above the dominant, turning a pedal point into a pedal chord.
- a mediant (3rd scale degree) pedal is only likely to appear in the middle voices, usually in sections where the harmony oscillates between I and vi/iii. (a good example of a mediant pedal is Laurie Anderson's O Superman)
- a subdominant (4th scale degree) pedal will sometimes happen in preparation for a strong perfect authentic cadence, due to the emphasis placed on the subdominant as a preparation for the dominant, or sometimes after said cadence by way of coda (a plagal "Amen" cadence), often involving modal mixture. (i'm pretty sure there's a good one near the end of the Hammerklavier)
- if there are any pieces with submediant or leading tone pedals i'm not aware of them
- ok i lied. there are submediant pedals all over the finale of beethoven's string quartet op. 59 no. 2
- a tonic pedal strongly confirms the key, particularly in a section where the harmony oscillates between I and IV (for an even stronger confirmation/stabilization use the tonic plus the dominant (see Schumann's Romanze op. 28 no. 2))
- a dominant pedal in an interior voice also confirms the key, particularly in a section where the harmony oscillates between I and V (see Schubert's Sonata d. 960)
- a dominant pedal in the bass increases tension, acting as a preparation for I (see the waldstein sonata)
if you're not writing music that adheres to common practice tonality you can do whatever makes sense according to the established "rules" of your piece though