Can you inspire without process? The obvious answer is “of course!”
Can you inspire through process? Also, yes, but only if it "fits" the team!

I have seen certain types of Leaders assume their tried and tested process is best, that it works for all types of person. I have seen such leaders then prescribe one-size-fits-alls solutions to diverse teams and cause those teams fall apart. Such leaders treat team members as interchangeable units, each one performing their tasks, and living their lives, in the same way - which of course is great if everyone is the same, but a complete disaster if you have a mix of neural-types, gender-perspectives, socio-economic backgrounds, ages and experiences. This is anti-diversity thinking.

I have seen anti-diversity thinking lead to serious friction in teams, especially with new leadership, and that friction has either led to the leadership "finding new opportunities" or a mass exodus of talent; the worst attrition I have seen was ~70% of a company. In each case, the problem was more about rigid thinking than poor processes; an "I know best" attitude, instead of engaging and listening and adapting, causing alienation with well trained, talented teams who (rightly) feel like they have more to offer than be a cog in the machine.

Conversely I have found that when we engage with the team members, if we listen and understand the problems, in much the same way that good product managers talk to clients, we get insights that allow alignment of business need (process) to actual high-velocity delivery (value).

Engaging with the talent this way, elevating them, and promoting their needs, allows us as leaders to understand the diverse needs of diverse teams. That understanding of need can then be used to inform job-specs, hiring practises, company marketing, as well as the wider process... feeding economic success. This is diversity thinking.

However, the engaged manager will also identify mismatches between company-value and an individual's goals, which can lead to friction and going separate ways - the least fun part of building top class teams - but this is often the best outcome for both the person leaving and the company as they can find somewhere that is more aligned to their needs and the company can probably move faster without them pulling in a counter direction.

It is only when a manager aligns an individual's goals with the company's needs that you produce truly awesome technology, outstanding individual-contributors outliers not withstanding. This pairing, this matching, needs to be authentic and real, not the sales- or appearances-lead "company values" or "personal goals" but the real goals and targets that are actually driving the executive team. If the company just wants to sell to private equity so the shareholders can cash out, state it, the team will work with that goal in mind - although they might ask for a bigger piece of the pie. A misalignment in company-goals vs personal-goals leads to friction, and ask yourself how can good teams resolve this if the company-goals are inauthentic?

It is easy to inspire, just be authentic and align talent with business value. But this requires that good managers are able to bend, to mould themselves to fit the individuals you’re trying to mentor/inspire. You do not need to dilute the business-need to achieve this, in fact, the business's needs should be front-and-centre so that individual contributors can get behind them. In exchange good manager need to get behind their staff, to make them feel listened to. But listening properly is a skill, and one which is not passive, you have to listen to their concerns and ideas, giving feedback to show that you’ve understood what they’ve said and taking action to build credibility. [^1] [^2]

I have seen time and time again where great, adaptive mangers help companies thrive, and seen previously great companies stagnate because of poor managers.

[^1]: Bernard T. Ferrari's article on The executive’s guide to better listening [^2]: To Be a Better Leader, Give Up Authority by Adhar, Hentrich, Hlupic