I think you are conflating two issues: aliasing and windowing.
Aliasing depends on the sampling frequency. Aliasing happens when input signals are present at the sampler with frequencies higher than the Nyquist rate, which is half the sampling frequency. Aliasing can be minimized by use of an anti-aliasing filter at the sampler input and with oversampling. When sampling an IF, the anti-aliasing filter might be a band-pass filter rather than low-pass.
Windowing depends on the total duration of the sampling window. Windowing reduces the spectral resolution of the DFT, when considered as an estimate of the spectrum of the input signal.
You can reduce the windowing effect by taking a longer sampling window, but of course that makes the measurement slower.
Analog spectrum analyzers also suffered from spectral leakage because IF bandpass filters cannot be made perfectly narrow. And similarly were able to obtain higher spectral resolution by reducing the "resolution bandwidth (RBW)" with the similar trade-off of slowing the measurement.
Practically, digital spectrum analyzers aren't designed to be ideal. They're designed to be better than the analog spectral analyzer they replaced, or to provide similar performance at a lower price. It's well known that the spectral resolution is limited, and its not expected to be able to perfectly reconstruct the input signal from the spectrum analyzer measurement.