[riptheworld]

Bitcoin’s throughput is limited as a function of network security and network delay. It has nothing to do with making it easier for clients to sync with the current state. You can improve Bitcoin’s transaction rate in two ways:

1.) decrease mining difficulty, i.e., the amount of hashing required to produce a valid proof-of-work on average. This impacts the security of the network.

2.) increase the block size so you can fit more transactions into a single block. This negatively impacts network latency (and therefore scalability, as it increases the burden of propagating messages across the network).

To your question on Algorand: yes, new consensus participants can quickly and easily sync with the current state of the blockchain through fast catch-up [1], without any meaningful security degradation [2].

[1] https://youtu.be/BOnond-J3Zo

[2] https://eprint.iacr.org/2018/269.pdf

[tromp]

So there's no way to trustlessly verify Algorand history; you have to trust a checkpoint, or trust some signatory quorum in some alternative design that's not even implemented yet.

[riptheworld]

You can trustlessly verify the entire Algorand history by verifying it yourself (same as Bitcoin). However, almost all blockchains (including Bitcoin) will suffer from this problem of longer and longer sync times, and so some bootstrapping solution is necessary.