---Emphasis added---if it's only the turns ratio that determines how much will be the voltage increase, why don't people just make the turns on the primary just be 1?
Succinctly, eschewal of 'all the ills' attending low impedance systems -- prominent among them being liability to core saturation and significant resistive losses (in both the primary winding and, to a greater extent, throughout the primary circuit)...
But to your broader question:
Please recall that 'turns ratio' is the sole Z-transformation determining 'factor' only where a pure (i.e. sinusoidal) signal acting 'through' a net-nonreactive system is manifest. -- As a practical matter, topologies exploitative of 'ΔI/ΔT transformation' (e.g. true flyback topologies) and/or 'resonant/periresonant transformation' (e.g. the circuit under discussion, Tesla coils, etc...) often (but not necessarily) in combination with mutual inductors marked by significant disparity in primary to secondary impedance ratios, offer --far and away-- the most efficient conversion schemes from a material (and, hence, mass) conservation standpoint...
While your (above quoted) suggestion is both intriguing and, perhaps, practically realizable -- Please bear in mind the fact that transformer efficiency declines abruptly with reduction in primary to secondary coupling -- topologies defined by mutual (or, for that matter, self) inductance are, of course, inconstant with significant 'flux leakage' (CIP 'leakage inductance') -- That said, your proposal is definitely worthy of further investigation!we could spread the transformer over that entire area to increase the distance between the wires. This would also help for cooling the transformer
Correct -- However thermal transfer is essential as well...About the potting is this to prevent sparking across wires for high voltage in the closely wound wires?