No It is not necessary to maintain similar level of throughput on all secondary indexes as of the throughput of the table
The write to the table will not throttled when it is not written in Index.
We set indexes on table for fast retrieval based on non-key attributes and some times those attributes need not to be added when adding row in a table, at that time item in index will not be written. And it is not necessary to provisioned the write capacity on index as of the write capacity of the table.
Please refer to the Global Secondary Indexes FAQ for details, specifically Can I provision throughput separately for the table and for each global secondary index?:
Yes. GSIs manage throughput independently of the table they are based
on. You need to explicitly specify the provisioned throughput for the
table and each associated GSI at creation time. [...]
Depending upon on your application, the request workload on a GSI can
vary significantly from that of the table or other GSIs. Some
scenarios that show this are given below: [...]
As your needs evolve, you can change the provisioned throughput of the
GSI, independently of the provisioned throughput of the table.