Strings as Primary Keys in SQL Database

Another issue with using Strings as a primary key is that because the index is constantly put into sequential order, when a new key is created that would be in the middle of the order the index has to be resequenced... if you use an auto number integer, the new key is just added to the end of the index.

Technically yes, but if a string makes sense to be the primary key then you should probably use it. This all depends on the size of the table you're making it for and the length of the string that is going to be the primary key (longer strings == harder to compare). I wouldn't necessarily use a string for a table that has millions of rows, but the amount of performance slowdown you'll get by using a string on smaller tables will be minuscule to the headaches that you can have by having an integer that doesn't mean anything in relation to the data.

Strings are slower in joins and in real life they are very rarely really unique (even when they are supposed to be). The only advantage is that they can reduce the number of joins if you are joining to the primary table only to get the name. However, strings are also often subject to change thus creating the problem of having to fix all related records when the company name changes or the person gets married. This can be a huge performance hit and if all tables that should be related somehow are not related (this happens more often than you think), then you might have data mismatches as well. An integer that will never change through the life of the record is a far safer choice from a data integrity standpoint as well as from a performance standpoint. Natural keys are usually not so good for maintenance of the data.

I also want to point out that the best of both worlds is often to use an autoincrementing key (or in some specialized cases, a GUID) as the PK and then put a unique index on the natural key. You get the faster joins, you don;t get duplicate records, and you don't have to update a million child records because a company name changed.

Inserts to a table having a clustered index where the insertion occurs in the middle of the sequence DOES NOT cause the index to be rewritten. It does not cause the pages comprising the data to be rewritten. If there is room on the page where the row will go, then it is placed in that page. The single page will be reformatted to place the row in the right place in the page. When the page is full, a page split will happen, with half of the rows on the page going to one page, and half going on the other. The pages are then relinked into the linked list of pages that comprise a tables data that has the clustered index. At most, you will end up writing 2 pages of database.