Its advantages are real: easier care, resistance to creasing and abrasion, a lower price. If you are buying a suit for one occasion a year and do not want to spend time looking after it, polyester is tempting.
Appearance in daylight matters too. Polyester more often has a noticeable sheen that looks artificial in bright sun and in photos. Not every polyester shines the same way, but the risk is higher. Wool has a more matte surface and a natural depth of colour, so navy looks like navy rather than navy with a glint. Synthetics also build up static more easily, especially in dry, air-conditioned rooms, and attract dust and lint.
Labels often show blends, for example wool with some polyester and elastane. A small share of polyester improves crease resistance, elastane adds a little stretch, and the cloth still behaves mostly like wool. The higher the share of polyester, the closer the fabric gets to a pure synthetic, breathability included. So read the proportions, not just the first word on the label.
To be fair, at a short event in an air-conditioned venue, when you drive there and do not stand in the sun for long, the difference is less noticeable. Problems start once you add sunshine, a walk, outdoor photos and several hours on the move.