How can pick up be better with a wider tyre (205 against 185) which has more contact & resistance with the road.
Answered your own question.... Cannot.
Want to improve pickup, reduce rim size (weight for weight, this is better), reduce rim weight, reduce tire profile (use 185 instead of 205).
However, these are the downside:
Less braking friction on dry road, less cornering stability,
Advantages:
Apart from the above, improve FC, improve hydroplaning resistance, improve comfort.
Like everything, it is a balancing equation. Choosing tire that has stiff sidewalls will also improve cornering slightly but at the cost of comfort.
I drive slow and corner slow. FC and wet performance are top priority. So I stay strictly to 185/65/R15.