If my Soil Health Card says all nutrients are sufficient, do I still need fertiliser?

Not quite, sufficient does not mean zero fertiliser. The card recommendation already takes your good soil status into account and will usually still suggest a reduced, balanced dose, especially for nitrogen, because crops remove nutrients as they grow and nitrogen in particular is used up and lost every season. So even with a healthy card you typically still apply nitrogen as the crop needs it, while you can cut back on phosphorus and potash if those are marked high, and skip micronutrients that are sufficient. The smart move is to follow the dose printed on the card, which is tuned to your soil, rather than the full blanket dose. This is where good soil saves you money, you buy fewer bags of DAP or potash without losing yield. Keep adding organic matter to maintain that healthy status. If you are unsure how far to reduce, confirm the exact dose with your KVK for your crop and target yield, and do not skip nitrogen entirely just because the card looks good.