`--mode reinstall` breaks regenerating lsp dids

when deploying the ledger locally using the ledger.private.did and after that swapping to ledger.public.did (no service arguments) and deploying a canister that has a dependency on the ledger, if i use
dfx deploy my_canister_that_depends_on_the_ledger --mode reinstall -y, the did file in .dfx/local/lsp/<ledger_canister_id>.did is not being updated to reflect the fact that no init args are needed. this leads to the motoko extension to complain.
if i use dfx deploy my_canister_that_depends_on_the_ledger instead, everything works as expected

I expected to see this happen:
the dids in the lsp folder are generated correctly, even if i use --mode reinstall

Instead, this happened:
the dids in the lsp folder still contain the service arguments, and therefore the motoko language extension complains.

Meta

dfx --version:

dfx 0.13.1

tagging @rvanasa as this might also interesting for him

Reproduce the issue by deploying the local ledger with ledger.private.did, switching to ledger.public.did, and running dfx deploy my_canister_that_depends_on_the_ledger --mode reinstall -y. Inspect .dfx/local/lsp/<ledger_canister_id>.did and compare it with a normal deployment; done means reinstall regenerates the DID without service arguments.