"The key challenge in scaling Lightning in a trust-free manner is the creation of Lightning channels for casual users. Signature-based factories (AKA other ideas for channel factories before this paper) appear to be inherently limited to creating at most tens or hundreds of Lightning channels per unspent transaction output (UTXO). In contrast, simple covenants (including those enabled by CheckTemplateVerify (CTV) or AnyPrevOut (APO)) would allow a single UTXO to create Lightning channels for millions of casual users.
The resulting covenant-based protocols also:
support resizing channels off-chain,
use the same capital to simultaneously provide in-bound liquidity to casual users and route unrelated payments for other users
charge casual users tunable penalties for attempting to put an old state on-chain, and
allow casual users to monitor the blockchain for just a few minutes every few months without employing a watchtower service.
As a result, adding CTV and/or APO to Bitcoin's consensus rules would go a long way toward making Lightning a widely-used means of payment
...
The remainder of this paper is organized as follows.
Section 2 demonstrates that the key challenge in scaling Lightning is providing Lightning channels to casual users while meeting their usability requirements.
Section 3 then shows why no protocol that uses Bitcoin's current consensus rules is likely to meet this challenge.
Covenant-based protocols for creating Lightning channels are presented in Section 4,
and they are analyzed in Section 5. The remaining sections look at related work and give conclusions."
This has been my reformatted for readability but otherwise mostly copy and paste of the introduction of " Scaling Lightning With Simple Covenants" paper written by John Law. I hope this introduction gets you as interested in reading the paper as it has gotten me.
The full paper can be read here: Scaling Lightning With Simple Covenants by John Law