The Intel 440LX chipset introduced the AGP-Slot for the first time. At that time graphic cards used the PCI bus for data transfer and there weren't any special power considerations for the AGP-Slot. Nearly all designers used the PCI power recommendation for the AGP Slot as well, which was ok at that design stage and suited all available AGP VGA cards.
Problems With The AGP-Power Supply
With the arrival of the Nvidia TnT chip this AGP power design had reached its limit. Many LX-systems with TnT either crashed during games or they didn't start at all. Some motherboard vendors modified the design for future revision of their 440LX motherboards, but most of them waited for the new 440BX design to implement a better AGP Slot power supply.
There are a couple of ways to fix the power consumption problem. First, provide a better power supply to the AGP Slot or connect the 3.3 V of the AGP Slot directly to the ATX Power Connector.
Alternatively, the 3D-chip makers shrunk the graphics chip e.g. from .25u to .18u. When a chip structure gets smaller, the power consumption at the same clock speed is reduced too. Both ways were used to tackle the graphics power consumption problem. The shrink of the graphics chip not only allows you to reduce the consumed power, the heat of the chip and the voltage, but also enables you to get a higher frequency out of the same design.
This brought the AGP-card back to the vicious circle of high power consumption plus heat spreading. Higher frequencies, more on chip features (like T&L), more memory and more graphic chips require more power and produce more heat, which in turn requires more cooling.