A few reasons.
First thing you need to know is that they'll advertise roles with a particular salary band, e.g. £48,000 - £58,000 for a Grade 7 role. What they don't tell you is that they'll automatically start you on the bottom of that salary range, and you won't move off the bottom of it due to the pay freeze. The only Grade 7s earning £58,000 are the ones who have been Grade 7s for a really long time and got automatic salary increases to move up the pay band before the pay freeze, which has been in place for over a decade now. This means that the most talented Grade 7s who are ready to be promoted to Grade 6 are still at the bottom of the pay band, and the people at the top of the pay band are the ones who have been bumbling along at the same level of seniority for 20 years because they either aren't very ambitious or aren't very good. It also means that when those talented Grade 7s get promoted to Grade 6 and have management responsibilities, they'll be earning about the same as those long term Grade 7s who never got promoted.
The process for getting promoted is incredibly slow. Although they don't tend to promote rubbish people in my experience, they will make talented people who are ready for promotion do two roles at Grade 7 before they'll consider them for a Grade 6 role. So that means it'll take you at least 6 years to get promoted from Grade 7 at £48,000 to Grade 6 on £60,000.
Another reason I wouldn't recommend it is that once you're in, it can be very difficult to get out. This is partly because you might end up doing something niche like bona vacantia which has no real equivalent in the private sector. But it's also due to a perception that the Government Legal Department is where legal careers go to die, and that the people who work there are no good and would never be able to hack it in private practice. For what it's worth I think this perception is very unfair. There are lots of very hardworking, talented lawyers there, many of whom trained and worked in top law firms beforehand. Again, this will depend massively on what job you are doing. So for example, when I worked there I was doing a general commercial role with a specialism in EU law issues, which was actually pretty valuable to private sector employers. I didn't have any problems getting out again when I wanted to. And my former boss is now head of public sector law at one of the Big 4. So it is possible. But it can be very hard.
I also hear that morale has taken a real nose dive in the last few years.