The sweet spot for an agile approach is to lock down time/cost, and deliver the highest value capabilities in an incremental fashion until time/money runs out (or there is money left but something more valuable to invest in).
During that time, if we have designed our incremental strategy well, we will realise actual business benefits/value for each increment we release. This will often create further funding for the “project”, should we wish to invest more.
So, the varying of (at least functional and operational) scope is ESSENTIAL to an agile approach. We can look to be a bit more concrete with the desired business capabilities we will deliver within the time/cost, but there MUST be flexibility in design and approach.
Attempts to fix time, cost AND functional/operational scope are a violation of sound project management principles, regardless of whether you are taking an agile approach or not. It’s ignorant at best, and negligent at worst.