Does an invitation letter make it harder to get a Japanese visa?

It is recommended to follow the official procedures and give only the requested documentation. Giving more than is required would seem odd. If it does appear suspicious, it will most likely be discarded. A person evaluating a visa application works to see if you qualify or pose a risk. The same would be true of other spurious information such as sending bank statements when none is required.

There are rules for qualifying for a visa and usually an application to fill out with a list of the required supporting documentation. Some countries ask for a letter of invitation but those actually a minority, usually countries who do generally do not welcome tourism. For those that do encourage tourism, then you are more likely to be asked about onward travel and proof of accommodation and those you must provide when required by the application.

As originally asked, you were asking a very general question, which made it hard to answer.

• When your itinerary and especially the financing of your visit depend on your host, that should be documented. Example: You have been invited to stay at the summer home owned by the parents of a friend from university. You are paying for the flight tickets, you are not expected to pay for room and board. Then they should put that in writing.
• It is unnecessary and even suspicious if people who do not contribute to your trip give assurances that you will behave properly as a tourist. They cannot know what you will do, so they can't make promises. Example: You want to go to Paris and also meet a friend in Nice for dinner. An invitation from that friend proves nothing.
• If you provide documents that are not required, you show that you do not understand the process. That's bad, because you might also misunderstand your rights and duties as a tourist (i.e. leave on time, do not work).

If the Japanese embassy website lists invitation letter in visa requirements then it's mandatory to provide it. Where invitation letter is required the usual practice is that it can either be a real person (friend, relative) or a tourist company you engage if your purpose is tourism (and buy a package). Yes, some countries put restrictions like buying a prepaid holiday package from registered tour agency in order to grant a tourist visa. Perhaps this applies to Colombian citizens intending to visit Japan for tourism. Do confirm with the embassy.