Basically, when it comes to growing plants, there are multiple things plants need to grow:
- light
- carbon (which means CO2 or a liquid carbon source)
- macro nutrients (nitrate, phosphate, potassium)
- micro nutrients (iron and all sorts of other trace elements)
Where planted tanks get into trouble is when those things aren't in balance. A low-light tank has only a little light, so plants grow slowly, which means they only use up carbon, macros, and micros in small amounts. In this scenario, the level of CO2 naturally dissolved in your aquarium water (from equilibrium with CO2 in the atmosphere) is adequate, fish poop etc. provides enough of the macro nutrients, and your regular water changes supply enough micro nutrients.
Now if you have a very high amount of light, that is going to make the plants want to grow really fast. Of course, plants need carbon to grow (carbon is the backbone of most cells). But plant growth at high lighting requires more carbon--more CO2--than the ambient levels in your water just from atmospheric CO2. In other words, you need to artificially inject more carbon into your water via a CO2 system. If you don't, then what will happen is you have all this light, but the plants can't grow and take advantage of it because there is no CO2 for them. So what will happen? Algae will take advantage of the fact there are unused nutrients, and lots of light, and you'll have an algae explosion.
The general principle is that if you are providing enough of everything in my bullet-point list above, and it is all relatively balanced, then plants have an advantage over algae, and you'll have lush plant growth and very minimal algae. However, if you have large amounts of some things (e.g. light) but are deficient in other things (e.g. CO2), then what happens is plants can't grow well and instead algae will begin to grow out of control.
That's the danger about putting 4 WPG on a tank with no CO2 injection. You are basically going to be creating a 26 gallon vat of algae. Which I don't think you want to do. Even 2.5 WPG (which is what you would be at with the 65W light) is really borderline...you might be able to get by without CO2 but you probably will have to dose some Flourish Excel (which is a liquid carbon source, roughly equivalent to having CO2) from time to time instead, and possibly may find yourself needing to do at least some minimal dosing of other ferts as well. I have a couple of tanks at 3 WPG and I dose Flourish Excel at every water change and occasionally dose other stuff as well.