There's a small misconception that the tx speed limit (throughput) on Arbitrum is capping the cost savings (already 90% lower than mainnet!)

But Arbitrum isn't running at capacity yet

The costs derive from posting data on L1 for security and will get more efficient over time Image
As the transactions on Arbitrum increase, the cost of generating a L1 batch of L2 transactions is spread across more transactions, lowering the per transaction cost

Additionally, things like BLS signatures hasn't been deployed just yet and neither has ETH2 data sharding
BLS signatures aggregates the signatures attached to user transactions together, decreasing the amount of data you have to put on the L1

ETH2 data sharding will increase the blockspace available on the L1 to post L2 transaction, lowering costs particularly as scale increases
Posting L2 transaction data to the L1 is important because it allows anyone in the world to reconstruct the current and historical state of the Arbitrum Rollup chain

Other approaches exist where this data is stored off-chain, but have different trust assumptions
Increasing the L2 Arbitrum speed limit will allow for more transactions to occur on L2, but because max capacity of Arbitrum One hasn't been reached yet, raising the speed limit today will not lower costs (and itself won't decrease the costs of posting data on L1)
The transactional speed limit starts to come into play when there is more demand than there is capacity, which is when gas prices on Arbitrum will start to increase using a EIP-1559 style gas auction mechanism
Think of it like this, Arbitrum today is a highway with 3 lanes and <1% congestion

Adding more 6 lanes to this highway (increase transaction throughput) doesn't matter until the exisiting lanes are congested when cars start to more more slowly (i.e when TXs become expensive)
However, as Arbitrum becomes more adopted and more cars (transactions) exist on the highway (L2 network), then adding more lanes (higher gas limit), will bring transaction costs back down to primarily the costs of posting data on the L1
Arbitrum's speed limit is currently set to match the throughout of Ethereum and will increase over time as the chain is time-tested in production more

It's primary purpose is to ensure validators can keep up with the chain and keep state bloat in check
Arbitrum can increase the transaction throughput to be much much faster than Ethereum

However, they can't just keep adding more lanes (raise throughput) to infinity because L1 blockspace to store tx data is finite (BLS and ETH2 come into play here)
Essentially, the costs of generating transactions on Arbitrum is derived primarily from the costs of batching and submitting L2 transactions onto the L1

Increased efficiency through more dense L1 data batching, BLS signatures, and ETH2 sharding is what will lower costs for users
TL;DR super bullish on Arbitrum and Rollups, but it's important to understand how they work and how exactly they will continue to decrease transaction costs over time

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