In testnet3, anyone can become a miner, it is possible to even mine a block on 
some CPU, because the difficulty can drop to one. In signet, we create some 
challenge, for example 1-of-2 multisig, that can restrict who can mine, so that 
chain can be "unreliably reliable". Then, my question is: why signets are 
introducing new coins out of thin air, instead of forming two-way peg-in 
between testnet3 and signet?

The lack of coins is not a bug, it is a feature. We have more halvings in 
testnet3 than in mainnet or signets, but it can be good, we can use this to 
see, what can happen with a chain after many halvings. Also, in testnet3 there 
is no need to have any coins if we are mining. Miners can create, move and 
destroy zero satoshis. They can also extend the precision of the coins, so a 
single coin in testnet3 can be represented as a thousand of coins in some 
signet sidechain.

Recently, there are some discussions regarding sidechains. Before they will 
become a real thing, running on mainnet, they should be tested. Nowadays, a 
popular way of testing new features is creating a new signet with new rules. 
But the question still remains: why we need new coins, created out of thin air? 
And even when some signet wants to do that, then why it is not pegged into 
testnet3? Then it would have as much chainwork protection as testnet3!

It seems that testnet3 is good enough to represent the main chain during 
sidechain testing. It is permissionless and open, anyone can start mining 
sidechain blocks, anyone with a CPU can be lucky and find a block with the 
minimal difficulty. Also, because of blockstorms and regular chain reorgs, some 
extreme scenarios, like stealing all coins from some sidechain, can be tested 
in a public way, because that "unfriendly and unstable" environment can be used 
to test stronger attacks than in a typical chain.

Putting that proposal into practice can be simple and require just creating one 
Taproot address per signet in testnet3. Then, it is possible to create one 
testnet transaction (every three months) that would move coins to and from 
testnet3, so the same coins could travel between many signets. New signets can 
be pegged in with 1:1 ratio, existing signets can be transformed into signet 
sidechains (the signet miners rule that chains, so they can enforce any 
transition rules they need).
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