There are plenty of reasons this is a terrible idea. Off the top of my head, here are a few of the most obvious...
It's bad for morale in multiple ways.
By looking for other, better jobs you're implying that you are unhappy in your current job, and that you think the things about your current job are so unlikely to change that the effort needed to make things work out is greater than the effort necessary to start over.
It also naturally raises questions with your other coworkers about whether you're leaving because you don't like them, or whether you think they're suckers for staying.
And it's demoralizing for the simple reason that you're going around telling people how much better everywhere else is, which- regardless of all the other concerns- is in itself a depressing thing to constantly be telling people. By telling people about other good jobs, you may even be motivating other employees to leave as well.
Motivating employees is difficult and expensive. Replacing employees is difficult and expensive. As a result, a large part of your manager's job is to keep and motivate employees. By demotivating your teammates and motivating them to leave, you are costing the company money in both the short and long terms, and actively working directly in opposition to your manager's goals.
It indicates to your manager that they need to replace you
Even if you're the only person on the team.
If you're looking for other jobs, and seem to be really excited about them, it's not unreasonable to assume that- one of these days- you're going to take one of those other jobs. The longer you stay on as an employee, the more valuable you become to the company, thanks to the on-the-job training you've received. Everything else being equal, if you've worked there for a year, and they suspect you'll leave within the next year, it makes no financial sense to keep you on for another year when they can replace you in a month with someone who's likely to stay for five or more years.
If you don't stay, the money invested in training you was a bad investment. They would be best suited forfeiting the sunk cost of training you and finding a replacement immediately.