If people skip Denmark entirely, that's one thing, but many of the companies trying to dodge taxes on lucrative exits were built on very generous government funds, and only dislike the Danish social model later, after having taken advantage of it for years when it suited them. For example, Playdead has received around $2m in government funds during the past few years, not to mention all the free health care for its employees. Now, its owners now are looking for ways to leave the country to lower taxes on a possible sale, which to many Danes seems like an attempt to cheat the system, against at least the spirit of the arrangement under which they accepted the funds.
There's your real problem right there: "Playdead has received around $2m in government funds"
Government "playing" Angel Investor. Every investor wants a maximum return on investment. Not so for government. They want to brag about how many companies they attracted (by changing the rules for some companies). This is where things can only go wrong.
