Every state in subset automaton is reachable
Any regular language is accepted by arbitrarily large automata with no inaccessible states. Let $M = (Q, \Sigma, \delta, q_0, F)$ be an automaton with no inaccessible states.  For any natural number $n$, we can write $[n]=\{0, \dots, n-1\}$ and define a new automaton

$$M_n = (Q\times [n], \Sigma, \delta_n, (q_0,0), F\times [n])\,,$$

where $\delta_n((q,i),\sigma) = (\delta(q,\sigma), i+1\bmod n)$ for any $q\in Q$, $i\in[n]$, $\sigma\in\Sigma$.

The effect is that each state counts modulo&nbsp;$n$ the number of characters that have been seen so far, but this has no effect on the behaviour of the automaton, other than making the state space bigger.

The automaton&nbsp;$M_n$ might have inaccessible states, so delete them. But note that, after reading any word of length $0\leq \ell&lt;n$, the automaton is in some state of the form $(q,\ell)$, so at least $n$&nbsp;states are accessible.  Setting $n = 2^{|Q|}$ gives you an exponentially bigger automaton, but why stop there? :-)

Thanks to @holf for the elegant fix to the problem of the disconnected state space.