Right, you seem to be confused as to what you are applying for and the neighbours role in things - and your Architect (who seems to be a plan monkey not an Architect) is probably to blame.
Permitted development (PD) is permitted and does not need any approval from the council, nor can any objections from neighbours prevent it. If designed within the criteria an extension can be built, and can be built where it might not otherwise be approved if formal permission was sought.
The Neighbour Consultation Scheme (NCS) for larger extensions is a way to ask the council if an extension larger than would otherwise be allowed under permitted development, would be allowed without having to apply for formal permission. Because it is larger than would otherwise be permitted development and may impact on neighbours then the neighbours get to comment. It's a comment, whether the neighbours phrase it as an objection or not, its still just a comment in planning terms. However the council will consider any comments and decide whether the comments are relevant or not and decide on that bases whether to deem the proposed works to need further and more detailed scrutiny under a formal planning application, or to deem comments insignificant and so allow the extension to be built without needing to apply for planning permission.
Then there is a traditional application for planning permission.
The issues for any competent designer to consider when advising clients is whether the extension can be built under PD and then no-one can stop it. The main issue is size and whether the size criteria for PD will meet the clients needs.
If a larger extension than allowed under PD is required, then the NCS can be used, but there is the risk that the impact on neighbours of a larger extension, may well cause adverse comments - and so the council may deem the impact too great to allow without further consideration.
So if an extension to meet the clients needs can't be built under PD and is not deemed suitable under NCS, then it needs formal planning permission. This then brings in the local planning policies and other considerations so the designer needs to design the extension to meet these requirements /restrictions. It's no good drawing up plans for an extension that wont meet policy, as it will not be approved.
So, taking all this into account, a competent designer will consider what the client wants and needs and advise them that their needs will be met under an extension that falls into one of the three categories above. The competent designer should also advise that if the extension that the client wants is in way contentions, then the best option is to build it (a smaller design if need be) under PD. The NCS is to some extents opportunistic, and may or may not be deemed acceptable - a cheap way to 'test the water'. However if an extension is not acceptable to the council or neighbours under the NCS then it is often unlikely that the same size extension would be approved if formal planning permission was applied for.