Oh, in fact there are many points
Paper bitcoins (or whatever) would allow physical exchange without anything going to the blockchain itself, ever. That would likely lead to higher awareness of common people about crypto and its advantages (you would be able to buy beer with it), thus promoting greater popularity of cryptocurrencies. From this perspective, it is a good thing
The problem arises when someone decides to create more paper bitcoins than there are real ones. But this issue can be dealt with if every paper bitcoin in existence means its digital version locked on the blockchain, the implication being that you can then spend only this paper bitcoins and can't create a transaction with their digital counterpart
TBH, this is kinda unexpected, coming from you that is.
This topic is probably one of the most argued--if a digital currency should have a physical form. So, I have a few questions: First of all, who would be the eligible person/company/group (whatever) to print out the said Cryptocurrency?
It doesn't really matter
Well, in the 19th century (before the Civil War) US banks had been issuing gold receipts (or how they were called), and this wasn't a problem as long as they didn't abuse their power, i.e. didn't issue more receipts than they had physical gold in their vaults (gold standard on a private level)
Obviously, they very soon started to exploit the popularity of these notes (I guess the origin of the term banknote refers to that period) by printing receipts not backed up by anything which led to bank runs and bankruptcies (probably another term originating in those times), but that's a different story
Secondly, let's say it is also in the form of a paper bill, how can we know the authenticity of the said paper bill? Thirdly, with the correlation of authenticity, who would clarify the number of existing paper Bitcoins or rather how could we know the number of existing paper Bitcoins?
I don't really know. But who could say some 20+ years ago that Bitcoin itself was possible (I refer to its decentralized nature mostly)? The thing is, if you can check the authenticity of a paper bitcoin, i.e. to check that it hasn't been spent by someone else, it's okay. In fact, there are OpenDime devices which serve as physical bitcoins, so we can actually say that there is a way to check that in a "provably fair" manner
And lastly with what you said:
"every paper bitcoin in existence means its digital version locked on the blockchain, the implication being that you can then spend only this paper bitcoins and can't create a transaction with their digital counterpart"
does that mean we should have a separate value for paper Bitcoins(?) as they cannot be transacted with their digital counterpart?
We don't need to, but technically, there will certainly be certain discrepancies - either premiums or discounts - depending on the ease of use and such things