So this is a theoretical question, did anyone even calculate the maximum possible growth rate of LN in such a way that the mainnet would work no less normally, without huge commissions [...]
Paul Sztorc (who thinks that Lightning alone can't solve the scaling problem, what is disputed by others) has calculated that
in the very best case, we could onboard 23,251 users per block, or about 2-3 million users per day. But that's of course not a realistic scenario: this would only be possible if 1) all block space was occupied by LN funding transactions and 2) if in each block, one single input spends to all channels in an enormous (non-standard) transaction.
It's more realistic to calculate a "maximum" value of around 3.000-5.000 channel openings per block, as a rule of thumb (that would be Taproot multisig transactions, with 250 to 300 vbytes each, which according to Sztorc can save over 100 vbytes when closing them compared to P2(W)SH).
But we further have to reduce this amount if we want a scenario like what you mention: that the "normal functioning" of the network is not affected and fees stay low.
The really heavy transactions in LN are the closing transactions, which can contain RSMCs ("commitment transactions", these include the penalty if your channel partner tries to cheat) and/or HTLCs (those in the case you only route a transaction from another sender to a receiver). You can see
at this page the expected weights of each Lightning-style commitment/HTLC transaction and output type. There are a lot of options, so the transaction can have different weights, but expect them in all cases to be larger than 500 vbytes, often larger than 1000.
Thus the number depends also on how many times channels would need to be closed. Channels could be open for years, or even infinitely, so we probably need much less closures than openings. I think it would be a good idea to "reserve" 20% of block space for channel closures. Let's reserve 50% additional space for other on-chain activity, so 30% would be left for LN onboarding.
My very rough estimation would be then that we can onboard LN users for about a third of the maximum number, or about 1500 per block. This is very optimistic but could be realistic once on-chain activity gets lower if LN is used for the majority of small to average payments.
1500 per block means 144 * 1500 = 216000 new channels a day, and thus around 78 million channels per year. Some users will have more than one channel, so I think a realistic absolute maximum for your scenario would be 150-200 million new users per year. Which is quite a lot, because e.g. from families not everybody needs a full Lightning node, and friends which trust themselves somewhat could use "LN accounts" (see
this concept) and/or channel factories.
(Edit: Made a mistake in my calculation - corrected it now
Numbers are now significantly lower, but I still think LN has not really a drastic growth problem)
