pressure needs to be applied to ASICs manufacturers to make miners that draw less power.
They already do. This is the main reason that people keep buying the newest generation of ASIC and that older generations become obsolete.
Miners have to pay for the electricity necessary for each hash. If they use less power per hash, then they can afford to buy more hashes and increase their share of the mining rewards.
Looking just at the Antminer S series, we can see that in 2013 they released the S1 with only 1.8 trillion hashes for each watt hour used. Over the next few years, they had reduced their power consumption to the point where the S8 could generate 36.7 trillion hashes with the same 1 watt hour. Today, the most efficient miners are calculating nearly 40 trillion hashes for each watt hour.
Miners will always demand more efficient mining rigs. Competition drives ASIC developers to produce the most efficient rigs that current technology makes possible. If they don't then some other ASIC manufacturer will produce a rig that is slightly more efficient and put them out of business. Regulations aren't going to be a stronger motivator than that.
Note that I'm talking about power in terms of how many hashes you can get from it. Just a straight limit to total power is useless. Miners will just buy more units (of the rigs that get the most hashes for that power). So the total power usage will stay the same.
In the end, it's the market value of a mined block and the cost of electricity that determines the total amount of money per hash that a miner can profitably spend on mining. Raise energy prices worldwide, and miners will use less energy overall. Decrease energy prices on renewables, and a larger percentage of mining will happen with renewable energy.
At the current difficulty it takes on average about 108 zetahashes (108,000,000,000,000,000,000,000 hashes) to solve a block, and the average block reward, including transaction fees, is about 6.75 BTC.
If the bitcoin exchange rate drops, then those 6.75 BTC won't be worth as much, so the block won't be worth as much. Also, in a few years after the next halving, the block won't be worth as many bitcoins. Both of these factors will result in some miners finding that they are earning less per block than they are spending on electricity (they are mining at a loss) and they will shut down rigs resulting in a reduction in energy usage.
On the other hand, if fees increase or if the exchange rate increases, then miners will find that they can afford to purchase more equipment and there will be an increase in energy usage.
If electricity gets cheaper, then miners can afford more electricity and therefore will buy more rigs. If electricity gets more expensive, then some miners will be mining at a loss and will shut down their equipment.
Note that the value of the network being secured directly affects the amount of money spent securing it (and therefore the amount of energy used to secure it). I don't think you can say the same about any Fiat currency.