|Yes it is safe to leave the charger on all the time.|
Modern litium ion technology is nothing like the old days of NiCads and nickel metal hydride technology. The same rules do not apply.
Lithium ion does not have a memory effect like the old NiCads and nickel metal hydride so you don't need to fully discharge before charging.
There are fail safe circuitries inside the batteries. With lithium ion, they are monitored very closely by the charging circuit.
Taking the battery out will not preserve life. You have a certain amount of charging cycles in a lithium ion. The average is 1000 full cycle charges. But you can also charge it 2000 times with a 50% charge 10,000 with a 10% charge, etc so even if you leave the battery in, it may trickle charge but it still follows the rule of how many times it can be charged.
"re-charging a battery that is'nt discharged was not recommended in the past"
That was the past. Lithium ion batteries are different then NiCads and don't follow that rule.