It much like the British empire in a way
Pax Romana, Pax Britannia!
Empires are tricky. You can conquer, but as Alexander the Great put it, 'only trade can hold it together'. Trade and cash, and comminications (as the excellent 'Worlds Busiest Railway Station on BBC2 reminded us, the railway was there to tie Imperial India together)
And the armies you create can make their own problems. The Army was very expensive, and didn't like to be bored (you dont want bored soldiers if your a Roman Emperor, because thats how you get your throat cut). so invading new places makes sense, especially since the Roman doctrine was 'its ours, we just havn't got there yet'. On the other hand, it can turn into a kind of Ponzi scheme. The more territory, the more resources, and possible taxes, and land for retired soldiers, etc. But that means longer borders, which means more soldiers, and more troops to occupy the region, etc, and the bigger chance of bordering people who really dont like you. And more money you need to spend.
Certainly the British Empire had this sort of problem - lots of red, but lots of places that put you in the red. If it hadn't been for India (which was a huge net producer of cash), the Empire would have been a net drain on resources in lots of territories. And bear in mind that empires are a bit haphazard in their growth - there is seldom a masterplan. The Roman Empire really starts by a relatively small city state going on the rampage, and then consolidating their position. Then rinse and repeat. The empire grew partially because those in charge needed a military victory to boost their political position, because some one needed the nice stuff someone else had, because why not?, etc. By the time Britain gets invaded, the Empire is huge, and every so often there is a certain amount of panic that the whole thing was overextended. Octavian was unhappy about his legions vanishing in the Tutenborg. Tiberius was worried about the Empire being just too big to survive, but Caligula wanted to invade Britain (he just ended up declaring war on Neptune, as you do). Claudius does invade, but the province almost goes under during the Boudiccan uprising. Trajan really goes for expansion, but then Hadrian consolidates, etc. And of course there is Persia. Rome and Persia are the two superpowers going up against each other - and its gets very nasty.
The Roman Army was
generally successful because they were professionals, with the kind of logistical support we'd expect today. Yes, lots of tribes etc would have a retinue of warrriors (often posh), and levies. But they tended to have to wander off to get the harvest in, etc. The Romans didn't have to do that. And generally their enemies didn't speed years practicing to do stuff. The famous Josephus quote say it all 'He would not err who described their exercises as battles without blood, and their battles as bloody exercises.' However, they didn't always win, and victory could be expensive. Much better to pay the top people off, and get them to rely on your support. After all, who else is going to get you those nice mosiacs in that new villa? And if your stroppy, then the legions are going to call round - so thats an interesting choice.
However, its all a bit of a con - you have to use the doctrine of concentration of forces, because there are generally a lot more of them than there are of you, and you just hope they dont figure that out. Once your embedded, then its much easier. Local kids join the Army, people get rich enough to go to the Senate, and evryone likes the wine which now cheap enough to import, or make enough money from exporting it to buy pepper and silks from India. And pay for the games to curry favour, to get you elected, to make you rich and powerful, etc.
Ultimately, the people in Britain often thought themselves Roman. By the end they used Roman money, had a church (which was a reinvention of the old imperial cult), had a means of admin in the Roman style, baths and games, and communicated in Latin. St Patrick was educated as a Roman would be. Were they Roman? Thats for them to say, but they often acted as though they were.
As for Horrible Histories - love them. My kids are total fans, and alas, when I talk in schoold, so are other kids (my gory stuff has been preempted by their gory stuff). Have a look on YouTube for the music vids - the Crassus one is ace, and he was indeed 'owned by the Persians', which shows that cash does not always equal military succes.