This article doesn't seem to be for any disk based structure but rather in-memory, in an in-memory scenario with order requirements some users have reported B-tree's as being quite competitive in mostly-read scenarios.
"Write-heavy" scenarios will probably be just fine with std::map (backed by an RB-tree) since the main downside of B-tree's is write amplification that isn't an issue since memory doesn't really have any block granularity.
LSM tree's in-memory will probably not be that useful as scanning becomes much more complicates (it's an interesting structure though if you have append-only workloads and want to implement dictionary for size-coded projects on top of a list).
LSMs are also useful for coping with (i.e., cleaning up the messes/consolidating no-longer-relevant historic events into just their final state) streaming/windowed multi-temporality as happens from lifting iterative/fixpoint computations from batch semantics to streaming/incremental updates.
You have to consolidate when the time has come to reclaim space and to avoid needless repeat compute during accesses. Might as well use it to run full LSM tactics. Especially when keeping in mind that array mapped trees have very simple index arithmetic once you treat them as semantically literally identical to a sorted (SoA) array with a cache-benefitting address/index scrambler.
We are talking about cache friendliness here, including compact data representation.
B-trees algorithm requires leaf nodes to be filled up to some prespecified fill factor, usually from 50% to 70%. This is not compact by any measures.
Both LSM trees and COLA allow for much more compact storage. They also pretty cache friendly in the "cache oblivious" sense.
Read up more on the COLA paper and funnily enough inspired by LSM-tree's I implemented something alike "basic-cola" a few months back (the thing I mentioned for size-coding), add to end of array, hierarchically re-sort for each of the bits of the new size that turns 0 from bottom up (divisible by 2, sort last 2, divisible by 4, sort last 4 and so on) and search with O((log2(n))^2) complexity.
B-tree fill factors are a parameter that can be tuned to avoid extra splits depending on your insertion patterns, an in-memory variant doesn't need to be tuned like a disk-based variation.
Also nothing preventing the "bottom" of an LSM variation to be a dense B-tree like structure that just gets less updates.
The COLA paper also never mentions threading, an in-memory B-tree should scale better with size if there is multi-threading while I don't see an easy way to avoid big locks with COLA, maybe why the COLA paper was from 2000 and we haven't seen much additional development on it? (LSM-tree's work beautifully of course but then you basically have the double-space issue like with semi-space garbage collectors).
In the end, what you choose is dependent on your application and patterns, COLA is a clever structure that probably shines in some scenarios.
Like my scenario was a mostly heavy on consecutive insertions as well as lookups of potentially arbitrary compound keys, perfect for cola like since those are cheap.
Extension of COLA called Fractal Indexes (on-disk storage) are commercialized by Tokutek: https://en.wikipedia.org/wiki/Fractal_tree_index