You know how Nyquist says you must sample at minimum twice your highest "frequency" or your get aliasing in your spectrum? It's the same with antennas except you must sample at least 1/2 your wavelength or you get grating lobes (the equivalent of aliasing) in you far field pattern; it's all the same math. A sample in time is equivalent to an antenna element sampling space. A big reflector is equivalent to sampling everything at once with no gaps; it's bandwidth independent. You can only put array element so close together, limited by the size of the element (itself is limited to a fraction of the lowest wavelength), electronics, and unwanted inter-element coupling (though there are tricks to take advantage of this coupling and make very wideband arrays).

If you leave "gaps" in your array elements, that's not a problem receiving strong, periodic signals. You can physically move the elements to fill in the gaps to remove those lobes; the equivalent of an equivalent time oscilloscope or a synthetic aperture radar. The problem is you can't do that when transmitting since you only have one opportunity to send something (non-periodic).

There are other disadvantages with phased arrays. Each amplifier has to be matched in amplitude and phase. I've had to bin lots of amplifiers as some have phase compression and some phase expansion over amplitude. That distorts the pattern over the pulse.

On the receive side, each receiver has thermal noise un-correlated with the others. So for N antenna elements, you received signal-to-noise scale proportional to sqrt(N) instead of N like you have on transmit, or with a big reflector. This is why arrays suck for very weak signals. Notice NASA keeps building big dishes for their DSN instead of "cheaper" arrays.

Then there's the whole timing and phase noise issue with distributing an oscillator.

Tough you can only make a reflector with about 100 dB gain.