The importance of logos can be a little tricky. There are several factors that play a role in how important your logo is to building a strong and healthy brand and how much is too much and too little.
Lots of people think a logo is the brand. This isn't entirely accurate. Logos are a large part of it, but they certainly are not the sum total of a brand.
While I can say without a doubt, logos are important, I think it is also fair to say that as brands grow and develop, there is room for their logo to grow and develop with them. For some brands, a logo has high importance from day one. For others, a logo may be important, but for a different reason and with room to grow as they do.
Most professional services businesses need a professionally designed logo from day 1. If these companies attempt to use a cheap, discount logo, they are communicating something about their own service. Growing, mature businesses tend to seek out growing, mature businesses to work with.
How would a business know if another business is growing and mature? They don't, they are simply going off whatever information they can find (which is typically a logo, website, business card, LinkedIn page or other social media and maybe some reviews) or a referral from their network. Even if it is a referral, that growing, mature business is going to be skeptical of a business that has a logo that is not professional looking.
(quick tip: In order to confirm your logo is of professional quality, you must hear that from a non-biased visual design professional. Your employees, anyone who is related to you, a vendor or someone who does not understand the principles of design does not count.)
Professional services businesses that don't take their logo serious will attract business from other businesses that don't care about how they present themselves. The business they get will be more likely to be difficult to deal with, complain about invoices and ask for more than they paid for. While this is a general statement, my experience has taught me that it is over true more than 70% of the time.
Let's look at an urgent care business. This type of company could likely get a discount logo without much of an impact on their business. No one is pre-shopping urgent cares and when someone needs an urgent care, they certainly aren't getting picky enough to judge the logo. In fact, most urgent care's don't even have a logo on the exterior of the building. Most people aren't going to see the logo until after the services are rendered. Even then, discount logos for medical services tend to look the same. It's hard to make a bad medical services logo... although they are out there.
Regardless of what business you are in, logos are going to have varying levels of importance and are going to need to accomplish different things at different times. Depending on your business, your budget and your goals, it might be best to do a design contest or it might be best to work directly with a creative agency or freelance designers. Its important that you are realistic about your logo and the business you are in. The best way to figure this out is to have a conversation with a design professional that knows the importance of a logo and what is the right fit for where your business is at.