These have the disadvantage that when overloaded by heavy rainfall, wastewater (with feces) ends up in the groundwater. Not so fresh! Moreover, sewers are more likely to get overloaded these days because there is much more road paving and tiling in cities, and climate change seems to make it rain more often and harder.
By disconnecting your home's downspouts, you ensure that rainwater that lands on the roof is diverted to the garden (and thus absorbed into the ground) or to a buffer system (e.g., a rain barrel). This reduces the burden on the sewer system during bad weather. Another benefit is that less, relatively clean rainwater is discharged to the treatment plant, which is better for the environment!
If you let rainwater run off into the garden, you contribute to maintaining the groundwater level. If you collect it, it can be used for various purposes: for flushing the toilet, for doing laundry (in the washing machine) and for watering the garden in periods of drought. Furthermore, it is also possible to make a water play system where you let the rainwater run to; this is great fun for children!
How to disconnect the downspout
In short, disconnecting has only advantages. Moreover, it is not at all difficult or complicated. The most important thing is to keep an eye on how the water is directed away from your home. This is to avoid moisture problems. Collect the water in a way that you prefer and that suits the available space in your yard.
Actual disconnection is really just a matter of cutting through the downspout and attaching a bend, pipe or other system, which directs the water away from the house. At what height to cut the pipe, of course, depends on your further plans. If you put a rain barrel under it, the pipe should be cut just above it and the bend attached so that the water flows easily into the barrel.
With a rain barrel, though, always make sure there is an overflow to another form of water collection, because a barrel doesn't have enough capacity during heavy rainfall either. For example, you can build a rainwater pond or an infiltration system. For infiltration in the garden, you can use buried infiltration crates. These collect the water and gradually lead it back into the soil. A gravel bed is also a convenient way to infiltrate. Make sure it slopes slightly away from the house.
Another possibility is to dig a trench or ditch, which leads water through the garden to a ditch, for example.
Infiltration capacity
Another important factor to consider when disconnecting the downspout and wanting the water to infiltrate into the garden is the capacity of the soil. If you have a clay soil in the garden, then the infiltration capacity of the subsoil is not that great and you will probably have to take extra measures to prevent your garden from becoming one big mud pool. You can dig extra trenches and apply provisions for collecting excess water. With a sandy soil, the water will sink quickly and thus the infiltration capacity is high.
So take a look at what possibilities your garden and its surroundings offer and make an appropriate plan accordingly!