"just compose a team" sounds easy, doesn't it? Unfortunately there are lots of failure modes involving different parts of the team not really understanding what each other are trying to do, let alone what they are doing, and subtle errors getting by people who don't know what to look for. So, you can find such teams and some of them work well but a lot of them don't.
So an alternate is to try and find or create domain experts who mix all the appropriate skills, but this is hard and in the extreme case involves chasing down unicorns.
Companies and industries flop back and forth between preferring different approaches - right now a lot of people are talking about "data scientists" as one of the latter, but it will likely change over time as it always does.
It's a hard problem, and it shows.
So why don't you just use the phrase "Why don't you just ...?"?
> There are so many more statisticians who can at least communicate and work effectively with developers and vice versa.
Not in my experience. You need to design your data infrastructure to promote easy analysis, and you need to design your models to scale well according to the amount of data you're working with. There are also many cases where a project will require mostly engineering work for a while, and then mostly analysis/statistics work–there are ways to handle this with specialists of course, but there's generally a significant switching cost.
Also people with a combination of statistics & programming aren't that rare–IMO it's more that employers tend to search for both degrees, when instead you should be trying to evaluate the skills directly.