A turbo is as close to a perpetual motion machine* as you can get. More exhaust pressure means more boost, means more air in the combustion chamber means more exhaust pressure...
It's effectively "free" power because you're already wasting engine power to push air out the exhaust ports. With a supercharger, you're adding an extra 15-30 hp load to the motor that wasn't there before. With an electric supercharger, you either need to source that 15-30 hp via a powerful alternator (at which point, you might as well have a direct belt drive instead) or you're continuously using an extra 5 hp or so to run the alternator to charge the batteries for the dozen seconds or so of boost you can actually use continuously.
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Formula 1's take is a good way forward... use a conventional turbo, but when you don't need the boost, convert exhaust pressure to electricity. Then use the stored electricity to help spool up the turbo faster (for extra power AND anti-lag purposes).
*Ignoring, of course, that none of this would happen without gasoline or diesel...
