Why is the correct cleanser important? For one major reason only. Acid mantle.
This is the natural oil-water barrier on the skin. It protects your skin from bacteria and prevents trans-epidermal water loss.
1. Protection from Bacteria
If you use a cleanser with a ph that is higher than your own skin, this will breakdown your acid mantle and make you susceptible to bacteria. So if you are acne prone, this is very important.
The skin has a ph of between 4.8 and 5.2. Most over the counter cleansers do not state the ph and others advertise a ph of 7, way too high for the skin.
So, ensure that the cleanser has a low ph, as is the case with cosmeceutical products
2. Trans epidermal water Loss
This occurs when the density of water in your skin is higher than in the outside atmosphere. If there are gaps in the acid mantle, the water will evaporate from your skin leaving your skin feeling dehydrated.
It also occurs when the bi-lipid layer is compromised.
3. Product penetration
You may have bought a really expensive night cream and now you want to "save" on your cleanser. This is a strategy that is often tried but results in poor product penetration of the active ingredients.
If the skin ph is out of balance you will not get optimal penetration of ingredients into the skin.
So, my advice is to start with the right cleanser and in many cases skin conditions such as acne prone skin or dehydration is resolved.