I enjoy project managing, but after doing a period of account management in parallel to it, I really disliked Account management. I did not enjoy dealing with customers, but I enjoyed working with my internal team to help deliver the project.
Moving forward, does an agile project manager need to have account management skills?
Yes. It will be an important skill: managing your client and their expectations.
In an Agile world, relationships are key. Since things are moving fast, they have the potential to break faster too. Hence the relationship will help you manage and grow your account.
You already build relationships with your team, but you find it hard to build a relationship with a customer. Perhaps someone has repeated the old saying "the customer is always right" once too often and you are now afraid to stand up for yourself: that's actually not uncommon, and customers know it too. That's why they sometimes act the way they do.
My view is that if you want to be a PM and the role needs you to deal with customers, there are strategies to cope with that. Assuming your company also employs sales people or people with "Account Manager" as part of their formal role, why not take them into customer meetings with you? It would be essential to brief them about the issues in advance, and most importantly, work out a strategy for dealing with the difficult situations that will inevitably arise, and predict how your customers are likely to react (especially to bad news). Think about how you want to respond to customer behaviours: maybe you can be flexible sometimes, while at other times, you need to put your foot down.
But also look for positive achievements that you can tell your customers, and win their trust. If you are only giving bad news, it's really tough out there. So don't just give bad news. Tell them about what you have achieved, what opportunities they will get from the things you are delivering, and make suggestions as to how to progress the project. Also ask for their help. People like to offer assistance, and it starts to make them part of your team, solving problems, instead of just throwing rocks at you while you sit and absorb the criticism.
So, back to your question: does an agile PM need account manager skills? - Yes, inevitably, but you can develop coping strategies and subcontract these skills to someone else until you have built your own confidence and can create the good working relationships that actually make the role feel rewarding. Use your wider team, and use the same interpersonal skills that make you a good delivery manager, and it will get easier.
No one comes to the table with all the strengths necessary to the be ideal project manager. Every PM practitioner out there--and I really mean 100% of them because it is a human condition of our significant inability to be perfect--has varying degrees of strength and gaps in knowledge, skills, and abilities to be a PM.
What is fantastic about your post is that you have identified and admitted to a weakness in your skill set, which is quite atypical in the can-do arrogance often exhibited. This means you have an opportunity to 1) grow this skill the best you can and 2) figure out how to cope with this missing attribute by delivering this capability in another way. Dealing with your account is extremely important so it will not be easy to resolve for you but it is not impossible to resolve, either.
Get comfortable with the fact you will never be great at all things PM. You will have areas at which you are an expert, areas you are okay, areas you are mediocre, and still other areas where you are incompetent. Do what you can on those weaker areas but become great and greater where your strengths are and find coping mechanisms for those other areas...like the rest of us.
I think it really depends on the size of the project/product and how it is defined. In my current company, TPM (tech side) do not have to manage CRM stuff and neither do the PMs. We as tech and tech-related teams need to dedicate ourselves to arriving at the best product. Again, this varies for companies of different sizes and responsibilities.
