The vast majority of economists subscribe today to the subjective theory of value that was in economics introduced by Jevons, Walras, and Menger. Subjective theory of value posits that value is subjective. A corollary to that is that there is no correct objective price.
However, if you talk about market price existing as an objective number that is different matter. A market price is defined as:
The last traded price or current good quotes by market-makers.
You can actually record market price in a way that everyone objectively agrees on it. Using the definition above I could check my local grocery store and record that the current market price of 2l milk is let's say 1.5 euro. Nobody can claim that that is the 'correct' or intrinsic price of milk, different people might have different valuation, but everyone, or at least every economist, can agree that is the 'current quote by market-maker' and thus that it is a market price.
The government (and most economically illiterate people) usually treat the market price as objective and ofter confound it with the price (the number) that a laber writes on it often ignoring that the owner is not the seller (someone sells at price X but I am not so that must say something about the market price of the asset I own)
No it seems that you confuse the concept of the 'right/correct/just/intrinsic price' which is inherently subjective with market price which is just last observable price at which someone transacted some item. Market price tells you only the lower boundary for valuation of buyer and upper boundary for valuation of seller, the valuation itself is subjective, but one can objectively record the market price at which transaction took place.
It is also government's prerogative to establish price controls. Government can declare that certain markets are subject to price floors or celling if they wish so. Or even set the prices outright like was done in USSR. A consensus among economists is that in most, but not all, markets pursuing price controls is bad policy that lowers economic welfare (see Mankiw Principles of Economics 5th ed pp 35 and pp 114-123), but still any sovereign government has ultimately the prerogative to set the price on any market as they wish regardless of whether you can sell something at that price or not.
To further illustrate the difference between value/willingness to buy (which is subjective) and market price (which is objective) I am also including the following diagram that hopefully explain it:
Willingness to Pay/Value: buyer’s maximum is called his willingness to
pay, and it measures how much that buyer values the good. (Mankiw Principles of Economics pp 139).
Market Price: The last traded price or current good quotes by market-makers.
This can be clearly visualized using demand-supply graph below:
The graph above visualizes willingness to pay for someone who is valuing the good more than market price (red), someone who is valuing the good for less than market price (green), these are not directly observable and they are based on people's values.
The market price (blue price) is price at which actually transaction happen in the market. Market price does not need to be equal to your personal subjective valuation (maybe your personal demand would be part of the total market demand somewhere below the market price as the green example in the picture above).
Why is market price objective? Because market price is factual and verifiable. For example, current market price of milk in Albert Hein online grocery market on 22/1/2021 is €1.75.
Anybody looking at the image below can see the price €1.75. Anyone can objectively verify that. It does not matter that you are not willing to pay €1.75. Your willingness to pay is subjective, but the market price of €1.75 is objective regardless whether you think that 2l milk has value of €10 or €0.5 (this is not directly observable and this valuation is only in your head). Bottom line, your personal valuation is not necessary the market price.
Anyone can agree that there is €1.75 at the picture. Unless you go as far as to deny existence of objective reality independent of humans that is.
Since there was some confusion about this, the above applies to both homogenous goods and heterogenous goods. Market prices for both are fully objective.
Here is example of heterogenous good, a unique painting selling for €770. Everyone can objectively agree that €770 is listed on the picture below. It is objective and empirically verifiable fact that the painting can be bought for €770. You might disagree with that price because your subjective valuation is different from market price, but the market price €770 is objective fact.